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Full text of "The seven follies of science; a popular account of the most famous scientific impossibilities and the attempts which have been made to solve them. To which is added a small budget of interesting paradoxes, illusions, and marvels"

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IN the following pages I have endeavored to give a sim- 
ple account of problems which have occupied the attention 
of the human mind ever since the dawn of civilization, and 
which can never lose their interest until time shall be no 
more. While to most persons these subjects will have but 
an historical interest, yet even from this point of view they 
are of more value than the history of empires, for they are 
the intellectual battlefields upon which much of our prog- 
ress in science has been won. To a few, however, some of 
them may be of actual practical importance, for although 
the schoolmaster has been abroad for these many years, it 
is an unfortunate fact that the circle-squarer and the per- 
petual-motion-seeker have not ceased out of the land. 

In these days of almost miraculous progress it is difficult 
to realize that there may be such a thing as a scientific im- 
possibility. I have therefore endeavored to point out 
where the line must be drawn, and by way of illustration 
I have added a few curious paradoxes and marvels, some 
of which show apparent contradictions to known laws of 
nature, but which are all simply and easily explained when 
we understand the fundamental principles which govern each 

In presenting the various subjects which are here dis- 
cussed, I have endeavored to use the simplest language 
and to avoid entirely the use of mathematical formulae, for 



I know by large experience that these are the bugbear of 
the ordinary reader, for whom this volume is specially in- 
tended. Therefore I have endeavored to state everything 
in such a simple manner that any one with a mere common 
school education can understand it. This, I trust, will ex- 
plain the absence of everything which requires the use of 
anything higher than the simple rules of arithmetic and the 
most elementary propositions of geometry. And even this 
I have found to be enough for many lawyers, physicians, 
and clergymen who, in the ardent pursuit of their profes- 
sions, have forgotten much that they learned at college. 
And as I hope to find many readers amongst intelligent 
mechanics, I have in some cases suggested mechanical 
proofs which any expert handler of tools can easily carry 

As a matter of course, very little originality is claimed 
for anything in the book, the only points that are new 
being a few illustrations of well-known principles, some of 
which had already appeared in " The Young Scientist " and 
" Self-education for Mechanics." Whenever the exact 
words of an author have been used, credit has always 
been given ; but in regard to general statements and ideas, 
I must rest content with naming the books from which I 
have derived the greatest assistance. Ozanam's " Recrea- 
tions in Science and Natural Philosophy," in the editions 
of Hutton (1803) and Riddle (1854), has been a storehouse 
of matter. Much has been gleaned from the " Budget of 
Paradoxes " by Professor De Morgan and also from Profes- 
sor W. W. R. Ball's " Mathematical Recreations and Prob- 
lems." Those who wish to inform themselves in regard to 
what has been done by the perpetual -motion -mongers must 
consult Mr. Dirck's two volumes entitled "Perpetuum 


Mobile " and I have made free use of his labors. To these 
and one or two others I acknowledge unlimited credit. 

Some of the marvels which are here described, although 
very old, are not generally known, and as they are easily 
put in practice they may afford a pleasant hour's amusement 
to the reader and his friends. 






Introductory Note i 

I Squaring the Circle 9 

II The Duplication of the Cube 30 

III The Trisection of an Angle 33 

IV Perpetual Motion 36 

V The Transmutation of Metals Alchemy 79 

VI The Fixation of Mercury 92 

VII The Universal Medicine and the Elixir of Life .... 95 


Perpetual or Ever-burning Lamps 100 

The Alkahest or Universal Solvent 104 

Palingenesy 106 

The Powder of Sympathy in 


The Fourth Dimension 117 

How a Space may be apparently Enlarged by merely chang- 
ing its Shape 126 

Can a Man Lift Himself by the Straps of his Boots? .... 128 

How a Spider Lifted a Snake 130 

How the Shadow may be made to move backward on the Sun- 
dial 133 

How a Watch may be used as a Compass 134 

Micrography or Minute Writing. Writing so fine that the 
whole Bible, if written in characters of the same size, 
might be inscribed twenty-two times on a square inch . . 136 



Illusions of the Senses 149 

Taste and Smell ... 15 

Sense of Heat 15 

Sense of Hearing 15 

Sense of Touch One Thing Appearing as Two 151 

How Objects may be apparently Seen through a Hole in the 

Hand 156 

How to See (apparently) through a Solid Brick 158 


The Chess-board Problem l6 3 

The Nail Problem l6 4 

A Question of Population J ^5 

How to Become a Millionaire l66 

The Actual Cost and Present Value of the First Folio Shake- 
speare l68 

Arithmetical Puzzles I 7 

Archimedes and His Fulcrum I7 1 





HE difficult, the dangerous, and the impossible have 
always had a strange fascination for the human 
mind. We see this every day in the acts of boys 
who risk life and limb in the performance of 
useless but dangerous feats, and amongst children of larger 
growth we find loop-the-loopers, bridge-jumpers, and all 
sorts of venture-seekers to whom much of the attraction 
of these performances is undoubtedly the mere risk that is 
involved, although, perhaps, to some extent, notoriety and 
money-making may contribute their share. Many of our 
readers will doubtless remember the words of James Fitz- 
James, in " The Lady of the Lake " : 

Or, if a path be dangerous known 
The danger's self is lure alone. 

And in commenting on the old-time game laws of England, 
Froude, the historian, says : " Although the old forest 
laws were terrible, they served only to enhance the excite- 
ment by danger." 

That which is true of physical dangers holds equally true 
in regard to intellectual difficulties. Professor De Mor- 
gan tells us, in his "Budget of Paradoxes," that he once 
gave a lecture on " Squaring the Circle" and that a 
gentleman who was introduced to it by what he said, re- 
marked loud enough to be heard by all around : " Only 


prove to me that it is impossible and I will set about it 
this very evening." 

Therefore it is not to be wondered at that certain very 
difficult, or perhaps impossible problems have in all ages 
had a powerful fascination for certain minds. In that 
curious olla podrida of fact and fiction, "The Curiosities 
of Literature," D'Israeli gives a list of six of these prob- 
lems, which he calls "The Six Follies of Science." I do 
not know whether the phrase " Follies of Science " origi- 
nated with him or not, but he enumerates the Quadrature 
of the Circle ; the Duplication, or, as he calls it, the 
Multiplication of the Cube ; the Perpetual Motion ; the 
Philosophical Stone ; Magic, and Judicial Astrology, as 
those known to him. This list, however, has no classical 
standing such as pertains to the " Seven Wonders of the 
World," the "Seven Wise Men of Greece," the "Seven 
Champions of Christendom," and others. There are some 
well-known follies that are omitted, while some authorities 
would peremptorily reject Magic and Judicial Astrology as 
being attempts at fraud rather than earnest efforts to dis-. 
cover and utilize the secrets of nature. The generally 
accepted list is as follows : 

1. The Quadrature of the Circle or, as it is called in 

the vernacular, " Squaring the Circle." 

2. The Duplication of the Cube. 

3. The Trisection of an Angle. 

4. Perpetual Motion. 

5. The Transmutation of the Metals. 

6. The Fixation of Mercury. 

7. The Elixir of Life. 

The Transmutation of the Metals, the Fixation of Mer- 
cury, and the Elixir of Life might perhaps be properly 


classed as one, under the head of the Philosopher's Stone, 
and then Astrology and Magic might come in to make up 
the mystic number Seven. 

The expression " Follies of Science " does not seem a 
very appropriate one. Real science has no follies. Neither 
can these vain attempts be called scientific follies because 
their very essence is that they are unscientific. Each one 
is really a veritable "Will-o'-the-Wisp " for unscientific 
thinkers, and there are many more of them than those that 
we have here named. But the expression has been adopted 
in literature and it is just as well to accept it. Those on 
the list that we have given are the ones that have become 
famous in history and they still engage the attention of a 
certain class of minds. It is only a few months since a 
man who claims to be a professional architect and techni- 
cal writer put forth an alleged method of " squaring the 
circle," which he claims to be " exact "; and the results of 
an attempt to make liquid air a pathway to perpetual 
motion are still in evidence, as a minus quantity, in the 
pockets of many who believed that all things are pos- 
sible to modern science. And indeed it is this false idea 
of the possibility of the impossible that leads astray the 
followers of these false lights. Inventive science has 
accomplished so much many of her achievements being 
so astounding that they would certainly have seemed 
miracles to the most intelligent men of a few generations 
ago that the ordinary mind cannot see the difference be- 
tween unknown possibilities and those things which well- 
established science pronounces to be impossible, because 
they contradict fundamental laws which are thoroughly 
established and well understood. 

Thus any one who would claim that he could make a 


plane triangle in which the three angles would measure 
more than two right angles, would show by this very claim 
that he was entirely ignorant of the first principles of 
geometry. The same would be true of the man who 
would claim that he could give, in exact figures, the diag- 
onal of a square of which the side is exactly one foot or 
one yard, and it is also true of the man who claims that 
he can give the exact area of a circle of which either the 
circumference or the diameter is known with precision. 
That they cannot both be known exactly is very well 
understood by all who have studied the subject, but that 
the area, the circumference, and the diameter of a circle 
may all be known with an exactitude which is far in 
excess of anything of which the human mind can form 
the least conception, is quite true, as we shall show when 
we come to consider the subject in its proper place. 

These problems are not only interesting historically 
but they are valuable as illustrating the vagaries of the 
human mind and the difficulties with which the early in- 
vestigators had to contend. They also show us the bar- 
riers over which we cannot pass, and they enforce the 
immutable character of the natural laws which govern 
the world around us. We hear much of the progress of 
science and of the changes which this progress has 
brought about, but these changes never affect the funda- 
mental facts and principles upon which all true science is 
based. Theories and explanations and even practical 
applications change or pass away, so that we know them 
no more, but nature remains the same throughout the 
ages. No new theory of electricity can ever take away 
from the voltaic battery its power, or change it in any 
respect, and no new discovery in regard to the constitution 


of matter can ever lessen the eagerness with which carbon 
and oxygen combine together. Every little while we 
hear of some discovery that is going to upset all our pre- 
conceived notions and entirely change those laws which 
long experience has proved to be invariable, but in 
every case these alleged discoveries have turned out to 
be fallacies. For example, the wonderful properties of 
radium have led some enthusiasts to adopt the idea 
that many of our old notions about the conservation of 
energy must be abandoned, but when all the facts are 
carefully examined it is found that there is no rational 
basis for such views. Upon this point Sir Oliver Lodge 
says : 

" There is absolutely no ground for the popular and gra- 
tuitous surmise that radium emits energy without loss or 
waste of any kind, and that it is competent to go on for- 
ever. The idea, at one time irresponsibly mooted, that it 
contradicted the principle of the conservation of energy, 
and was troubling physicists with the idea that they must 
overhaul their theories a thing which they ought always 
to be delighted to do on good evidence this idea was a 
gratuitous absurdity, and never had the slightest founda- 
tion. It is reasonable to suppose, however, that radium 
and the other like substances are drawing upon their own 
stores of internal atomic energy, and thereby gradually dis- 
integrating and falling into other and ultimately more stable 
forms of matter." 

One would naturally suppose that the extensive diffusion 
of sound scientific knowledge which has taken place during 
the century just past, would have placed these problems 
amongst the lumber of past ages ; but it seems that some 
of them, particularly the squaring of the circle and per- 
petual motion, still occupy considerable space in the atten- 
tion of the world, and even the futile chase after the 


"Elixir of Life" has not been entirely abandoned. In- 
deed certain professors who occupy prominent official po- 
sitions, assert that they have made great progress towards 
its attainment. In view of such facts one is almost driven 
to accept the humorous explanation which De Morgan has 
offered and which he bases on an old legend relating to the 
famous wizard, Michael Scott. The generally accepted 
tradition, as related by Sir Walter Scott in his notes to 
the " Lay of the Last Minstrel," is as follows : 

" Michael Scott was, once upon a time, much embar- 
rassed by a spirit for whom he was under the necessity of 
rinding constant employment. He commanded him to 
build a 'cauld,' or darn head across the Tweed at Kelso ; 
it was accomplished in one night, and still does honor to 
the infernal architect. Michael next ordered that Eildon 
Hill, which was then a uniform cone, should be divided 
into three. Another night was sufficient to part its summit 
into the three picturesque peaks which it now bears. At 
length the enchanter conquered this indefatigable demon, 
by employing him in the hopeless task of making ropes out 
of sea-sand." 

Whereupon De Morgan offers the following exceedingly 
interesting continuation of the legend : 

" The recorded story is that Michael Scott, being bound 
by contract to procure perpetual employment for a num- 
ber of young demons, was worried out of his life in invent- 
ing jobs for them, until at last he set them to make ropes 
out of sea-sand, which they never could do. We have 
obtained a very curious correspondence between the wizard 
Michael and his demon slaves ; but we do not feel at liberty 
to say how it came into our hands. We much regret that 
we did not receive it in time for the British Association. 
It appears that the story, true as far as it goes, was never 
finished. The demons easily conquered the rope difficulty, 
by the simple process of making the sand into glass, and 


spinning the glass into thread which they twisted. Michael, 
thoroughly disconcerted, hit upon the plan of setting some 
to square the circle, others to find the perpetual motion, 
etc. He commanded each of them to transmigrate from 
one human body into another, until their tasks were done. 
This explains the whole succession of cyclometers and all 
the heroes of the Budget. Some of this correspondence is 
very recent; it is much blotted, and we are not quite sure 
of its meaning. It is full of figurative allusions to driving 
something illegible down a steep into the sea. It looks 
like a humble petition to be allowed some diversion in the 
intervals of transmigration; and the answer is: 

" 'Rumpat et serpens iter institutum* 

a line of Horace, which the demons interpret as a direction 
to come athwart the proceedings of the Institute by a sly 

And really those who have followed carefully the history 
of the men who have claimed that they had solved these 
famous problems, will be almost inclined to accept De 
Morgan's ingenious explanation as something more than a 
mere " skit." The whole history of the philosopher's stone, 
of machines and contrivances for obtaining perpetual motion, 
and of circle-squaring, is permeated with accounts of the 
most gross and obvious frauds. That ignorance played an 
important part in the conduct of many who have put forth 
schemes based upon these pretended solutions is no doubt 
true, but that a deliberate attempt at absolute fraud was the 
mainspring in many cases cannot be denied. Like Dou- 
sterswivel\s\ "The Antiquary," many of the men who ad- 
vocated these delusions may have had a sneaking suspicion 
that there might be some truth in the doctrines which they 
promulgated ; but most of them knew that their particular 
claims were groundless, and that they were put forward for 
the purpose of deceiving some confiding patron from whom 


they expected either money or the credit and glory of having 
done that which had been hitherto considered impossible. 

Some of the questions here discussed have been called 
" scientific impossibilities " an epithet which many have 
considered entirely inapplicable to any problem, on the 
ground that all things are possible to science. And in 
view of the wonderful things that have been accomplished 
in the past, some of my readers may well ask : "Who shall 
decide when doctors disagree ? " 

Perhaps the best answer to this question is that given by 
Ozanam, the old historian of these and many other scientific 
puzzles. He claimed that " it was the business of the 
Doctors of the Sorbonne to discuss, of the Pope to decide, 
and of a mathematician to go straight to heaven in a per- 
pendicular line ! " 

In this connection the words of De Morgan have a deep 
significance. Alluding to the difficulty of preventing men 
of no authority from setting up false pretensions and the 
impossibility of destroying the assertions of fancy specula- 
tion, he says : " Many an error of thought and learning has 
fallen before a gradual growth of thoughtful and learned 
opposition. But such things as the quadrature of the circle, 
etc., are never put down. And why ? Because thought 
can influence thought, but thought cannot influence self- 
conceit ; learning can annihilate learning ; but learning 
cannot annihilate ignorance. A sword may cut through an 
iron bar, and the severed ends will not reunite ; let it go 
through the air, and the yielding substance is whole again 
in a moment." 



NDOUBTEDLY one of the reasons why this 
problem has received so much attention from 
those whose minds certainly have no special lean- 
ing towards mathematics, lies in the fact that 
there is a general impression abroad that the governments 
of Great Britain and France have offered large rewards for 
its solution. De Morgan tells of a Jesuit who came all the 
way from South America, bringing with him a quadrature 
of the circle and a newspaper cutting announcing that a 
reward was ready for the discovery in England. As a 
matter of fact his method of solving the problem was 
worthless, and even if it had been valuable, there would 
have been no reward. 

Another case was that of an agricultural laborer who 
spent his hard-earned savings on a journey to London, car- 
rying with him an alleged solution of the problem, and who 
demanded from the Lord Chancellor the sum of one hun- 
dred thousand pounds, which he claimed to be the amount 
of the reward offered and which he desired should be 
handed over forthwith. When he failed to get the money 
he and his friends were highly indignant and insisted that 
the influence of the clergy had deprived the poor man of 
his just deserts ! 

And it is related that in the year 1788, one of these de- 
luded individuals, a M. de Vausenville, actually brought an 



action against the French Academy of Sciences to recover 
a reward to which he felt himself entitled. It ought to be 
needless to say that there never was a reward offered 
for the solution of this or any other of the problems which 
are discussed in this volume. Upon this point De Mor- 
gan has the following remarks : 

" Montucla says, speaking of France, that he finds three 
notions prevalent among the cyclometers [or circle-squar- 
ers]: i. That there is a large reward offered for success; 

2. That the longitude problem depends on that success; 

3. That the solution is the great end and object of geometry. 
The same three notions are equally prevalent among the 
same class in England. No reward has ever been offered 
by the government of either country. The longitude 
problem in no way depends upon perfect solution; existing 
approximations are sufficient to a point of accuracy far 
beyond what can be wanted. And geometry, content with 
what exists, has long pressed on to other matters. Some- 
times a cyclometer persuades a skipper, who has made land 
in the wrong place, that the astronomers are in fault for 
using a wrong measure of the circle ; and the skipper thinks 
it a very comfortable solution! And this is the utmost 
that the problem ever has to do with longitude." 

In the year 1775 the Royal Academy of Sciences of 
Paris passed a resolution not to entertain communications 
which claimed to give solutions of any of the following 
problems : The duplication of the cube, the trisection of 
an angle, the quadrature of a circle, or any machine an- 
nounced as showing perpetual motion. And we have 
heard that the Royal Society of London passed similar 
resolutions, but of course in the case of neither society did 
these resolutions exclude legitimate mathematical investi- 
gations the famous computations of Mr. Shanks, to 
which we shall have occasion to refer hereafter, were sub- 
mitted to the Royal Society of London and published in 


their Transactions. Attempts to "square the circle," 
when made intelligently, were not only commendable but 
have been productive of the most valuable results. At the 
same time there is no problem, with the possible exception 
of that of perpetual motion, that has caused more waste of 
time and effort on the part of those who have attempted 
its solution, and who have in almost all cases been ignorant 
both of the nature of the problem and of the results which 
have been already attained. From Archimedes down 
to the present time some of the ablest mathemati- 
cians have occupied themselves with the quadrature, or, 
as it is called in common language, "the squaring of the 
circle " ; but these men are not to be placed in the same 
class with those to whom the term " circle-squarers " is 
generally applied. 

As already noted, the great difficulty with most circle- 
squarers is that they are ignorant both of the nature of 
the problem to be solved and of the results which have 
been already attained. Sometimes we see it explained as 
the drawing of a square inside a circle and at other times 
as the drawing of a square around a circle, but both these 
problems are amongst the very simplest in practical geo- 
metry, the solutions being given in the sixth and seventh 
propositions of the Fourth Book of Euclid. Other defini- 
tions have been given, some of them quite absurd. Thus 
in France, in 1753, M. de Causans, of the Guards, cut a 
circular piece of turf, squared it, and from the result de- 
duced original sin and the Trinity. He found out that the 
circle was equal to the square in which it is inscribed, and 
he offered a reward for the detection of any error, and ac- 
tually deposited 10,000 francs as earnest of 300,000. But 
the courts would not allow any one to recover. 


In the last number of the Athenaeum for 1855 a corres- 
pondent says " the thing is no longer a problem but an 
axiom." He makes the square equal to a circle by making 
each side equal to a quarter of the circumference. As De 
Morgan says, he does not know that the area of the circle 
is greater than that of any other figure of the same cir- 

Such ideas are evidently akin to the poetic notion of the 
quadrature. Aristophanes, in the "Birds," introduces a 
geometer, who announces his intention to make a square 
circle. And Pope in the "Dunciad" delivers himself as 
follows : 

Mad Mathesis alone was unconfined, 
Too mad for mere material chains to bind, 
Now to pure space lifts her ecstatic stare, 
Now, running round the circle, finds it square. 

The author's note explains that this "regards the wild 
and fruitless attempts of squaring the circle." The poetic 
idea seems to be that the geometers try to make a square 

As stated by all recognized authorities, the problem is 
this : To describe a square which shall be exactly equal in 
area to a given circle. 

The solution of this problem may be given in two ways: 

(1) the arithmetical method, by which the area of a circle 
is found and expressed numerically in square measure, and 

(2) the geometrical quadrature, by which a square, equal in 
area to a given circle, is described by means of rule and 
compasses alone. 

Of course, if we know the area of the circle, it is 
easy to find the side of a square of equal area ; this can be 
done by simply extracting the square root of the area, pro- 


vided the number is one of which it is possible to extract 
the square root. Thus, if we have a circle which contains 
100 square feet, a square with sides of 10 feet would be 
exactly equal to it. But the ascertaining of the area of the 
circle is the very point where the difficulty comes in ; the 
dimensions of circles are usually stated in the lengths of 
the diameters, and when this is the case, the problem re- 
solves itself into another, which is : To find the area of a 
circle when the diameter is given. 

Now Archimedes proved that the area of any circle is 

equal to that of a triangle whose base has the same - 
length as the circumference and whose altitude or height 
is equal to the radius. Therefore if we can find the length 
of the circumference when the diameter is given, we are in 
possession of all the points needed to enable us to " square 
the circle." 

In this form the problem is known to mathematicians as 
that of the rectification of the curve. 

In a practical form this problem must have presented 
itself to intelligent workmen at a very early stage in the 
progress of operative mechanics. Architects, builders, 
blacksmiths, and the makers of chariot wheels and vessels 
of various kinds must have had occasion to compare the 
diameters and circumferences of round articles. Thus 
in I Kings, vii, 23, it is said of Hiram of Tyre that "he 
made a molten sea, ten cubits from the one brim to the 
other; it was round all about * * * and a line of 
thirty cubits did compass it round about," from which it 
has been inferred that among the Jews, at that time, the 
accepted ratio was 3 to I, and perhaps, with the crude 
measuring instruments of that age, this was as near as could 
be expected. And this ratio seems to have been accepted 


by the Babylonians, the Chinese, and probably also by the 
Greeks, in the earliest times. At the same time we must 
not forget that these statements in regard to the ratio 
come to us through historians and prophets, and may not 
have been the figures used by trained mechanics. An 
error of one foot in a hoop made to go round a tub or cis- 
tern of seven feet in diameter, would hardly be tolerated 
even in an apprentice. 

The Egyptians seem to have reached a closer approxima- 
tion, for from a calculation in the Rhind papyrus, the ratio of 
3. 1 6 to I seems to have been at one time in use. It is prob- 
able, however, that in these early times the ratio accepted 
by mechanics in general was determined by actual meas- 
urement, and this, as we shall see hereafter, is quite 
capable of giving results accurate to the second fractional 
place, even with very common apparatus. 

To Archimedes, however, is generally accorded the 
credit of the first attempt to solve the problem in a 
scientific manner ; he took the circumference of the circle 
as intermediate between the perimeters of the inscribed 
and the circumscribed polygons, and reached the conclusion 
that the ratio lay between 3^ and 3^, or between 3.1428 
and 3.1408. 

This ratio, in its more accurate form of 3.141592 . . is 
now known by the Greek letter TT (pronounced like the 
common word pie), a symbol which was introduced by 
Euler, between 1737 and 1748, and which is now adopted 
all over the world. I have, however, used the term ratio, 
or value of the ratio instead, throughout this chapter, as 
probably being more familiar to my readers. 

Professor Muir justly says of this achievement of 
Archimedes, that it is " a most notable piece of work ; the 


immature condition of arithmetic, at the time, was the only 
real obstacle preventing the evaluation of the ratio to any 
degree of accuracy whatever." 

And when we remember that neither the numerals now 
in use nor the Arabic numerals, as they are usually called, 
nor any system equivalent to our decimal system, was 
known to these early mathematicians, such a calculation 
as that made by Archimedes was a wonderful feat. 

If any of my readers, who are familiar with the Hebrew 
or Greek numbers, and the mode of representing them by 
letters, will try to do any of those more elaborate sums 
which, when worked out by modern methods, are mere 
child's play in the hands of any of the bright scholars in 
our common schools, they will fully appreciate the diffi- 
culties under which Archimedes labored. 

Or, if ignorant of Greek and Hebrew, let them try it 
with the Roman numerals, and multiply XCVIII by 
MDLVII, without using Arabic or common numerals. 
Professor McArthur, in his article on " Arithmetic " in the 
Encyclopaedia Britannica, makes the following statement 
on this point : 

" The methods that preceded the adoption of the Arabic 
numerals were all comparatively unwieldy, and very simple 
processes involved great labor. The notation of the Ro- 
mans, in particular, could adapt itself so ill to arithmetical 
operations, that nearly all their calculations had to be 
made by the abacus. One of the best and most manage- 
able of the ancient systems is the Greek, though that, too, 
is very clumsy." 

After Archimedes, the most notable result was that 
given by Ptolemy, in the " Great Syntaxis." He made 
the ratio 3.141552, which was a very close approximation. 

For several centuries there was little progress towards 


a more accurate determination of the ratio. Among the 
Hindoos, as early as the sixth century, the now well-known 
value, 3.1416, had been obtained by Arya-Bhata, and a 
little later another of their mathematicians came to the 
conclusion that the square root of 10 was the true value 
of the ratio. He was led to this by calculating the perim- 
eters of the successive inscribed polygons of 12, 24, 48, 
and 96 sides, and finding that the greater the number of 
sides the nearer the perimeter of the polygon approached 
the square root of 10. He therefore thought that the 
perimeter or circumference of the circle itself would be the 
square root of exactly 10. It is too great, however, being 
3.1622 instead of 3.14159. . . The same idea is attrib- 
uted to Bovillus, by Montucla. 

By calculating the perimeters of the inscribed and cir- 
cumscribed polygons, Vieta (1579) carried his approxima- 
tion to ten fractional places, and in 1585 Peter Metius, 
the father of Adrian, by a lucky step reached the now 
famous fraction -||J, or 3.14159292, which is correct to the 
sixth fractional place. The error does not exceed one part 
in thirteen millions. 

At the beginning of the seventeenth century, Ludolph 
Van Ceulen reached 35 places. This result, which " in his 
life he found by much labor," was engraved upon his 
tombstone in St. Peter's Church, Leyden. The monu- 
ment has now unfortunately disappeared. 

From this time on, various mathematicians succeeded, 
by improved methods, in increasing the approximation. 
Thus in 1705, Abraham Sharp carried it to 72 places; 
Machin (1706) to 100 places; Rutherford (1841) to 208 
places, and Mr. Shanks in 1853, to 607 places. The 
same computer in 1873 reached the enormous number of 
707 places. 


Printed in type of the same size as that used on this 
page, these figures would form a line nearly six feet long. 

As a matter of interest I give here the value of the 
ratio of the circumference to the diameter, to 127 places : 

3.14159 26535 89793 23846 26433 83279 50288 41971 
69399 375 10 58209 74944 59230 78164 06286 20899 
86280 34825 34211 7067982148 08651 32723 06647 
0938446 + 

The degree of accuracy which may be attained by using 
a ratio carried to only ten fractional places, far exceeds 
anything that can be required in even the finest work, and 
indeed it is beyond anything attainable by means of our 
present tools and instruments. For example : If the 
length of a curve of 100 feet radius were determined by 
a value of ten fractional places, the result would not err 
by the one-millionth part of an inch, a quantity which is 
quite invisible under the best microscopes of the present 
day. This shows us that in any calculations relating to 
the dimensions of the earth, such as longitude, etc., we 
have at our command, in the 127 places of figures 
given above, an exactness which for all practical purposes 
may be regarded as absolute. This will be best appre- 
ciated by a consideration of the fact that if the earth were 
a perfect sphere and if we knew its exact diameter, we 
could calculate so exactly the length of an iron hoop which 
would go round it, that the difference produced by a 
change of temperature equal to the millionth of a millionth 
part of a degree Fahrenheit, would far exceed the error 
arising from the difference between the true ratio and the 
result thus reached. 

Such minute quantities are far beyond the powers of 
conception of even the most thoroughly trained human 


mind, but when we come to use six and seven hundred 
places the results are simply astounding. Professor 
De Morgan, in his " Budget of Paradoxes," gives the fol- 
lowing illustration of the extreme accuracy which might be 
attained by the use of 607 fractional places, the highest 
number which had been reached when he wrote : 

" Say that the blood-globule of one of our animalcules 
is a millionth of an inch in diameter. 1 Fashion in thought 
a globe like our own, but so much larger that our globe is 
but a blood-globule in one of its animalcules ; never mind the 
microscope which shows the creature being rather a bulky 
instrument. Call this the first globule above us. Let the 
first globe above us be but a blood-globule, as to size, in the 
animalcule of a still larger globe, which call the second 
globe above us. Go on in this way to the twentieth globe 
above us. Now, go down just as far on the other side. 
Let the blood-globule with which we started be a globe 
peopled with animals like ours, but rather smaller, and 
call this the first globe below us. This is a fine stretch of 
progression both ways. Now, give the giant of the twen- 
tieth globe above us the 607 decimal places, and, when he 
has measured the diameter of his globe with accuracy 
worthy of his size, let him calculate the circumference of 
his equator from the 607 places. Bring the little phil- 
osopher from the twentieth globe below us with his very 
best microscope, and set him to see the small error which 

1 What follows is an exceedingly forcible illustration of an important 
mathematical truth, but at the same time it may be worth noting that 
the size of the blood-globules or corpuscles has no relation to the 
size of the animal from which they are taken. The blood corpuscle 
of the tiny mouse is larger than that of the huge ox. The smallest 
blood corpuscle known is that of a species of small deer, and the 
largest is that of a lizard-like reptile found in our southern waters 
the amphiuma. 

These facts do not at all affect the force or value of De Morgan's 
mathematical illustration, but I have thought it well to call the atten- 
tion of the reader to this point, lest he should receive an erroneous 
physiological idea. 


the giant must make. He will not succeed, unless his 
microscopes be much better for his size than ours are for 

It would of course be impossible for any human mind to 
grasp the range of such an illustration as that just given. 
At the same time these illustrations do serve in some 
measure to give us an impression, if not an idea, of the 
vastness on the one hand and the minuteness on the other 
of the measurements with which we are dealing. I there- 
fore offer no apology for giving another example of the 
nearness to absolute accuracy with which the circle has 
been " squared/' 

It is common knowledge that light travels with a ve- 
locity of about 185,000 miles per second. In other words, 
light would go completely round the earth in a little more 
than one-eighth of a second, or, as Herschel puts it, in less 
time than it would take a swift runner to make a single 
stride. Taking this distance of 185,000 miles per second 
as our unit of measurement, let us apply it as follows : 

It is generally believed that our solar system is but an 
individual unit in a stellar system which may include hun- 
dreds of thousands of suns like our own, with all their 
attendant planets and moons. This stellar system again 
may be to some higher system what our solar system is to 
our own stellar system, and there may be several such 
gradations of systems, all going to form one complete whole 
which, for want of a better name, I shall call a universe. 
Now this universe, complete in itself, may be finite and 
separated from all other systems of a similar kind by an 
empty space, across which even gravitation cannot exert its 
influence. Let us suppose that the imaginary boundary of 
this great universe is a perfect circle, the extent of which 


is such that light, traveling at the rate we have named 
(185,000 miles per second), would take millions of millions 
of years to pass across it, and let us further suppose that 
we know the diameter of this mighty space with perfect 
accuracy ; then, using Mr. Shanks' 707 places of decimal 
fractions, we could calculate the circumference to such a 
degree of accuracy that the error would not be visible under 
any microscope now made. 

An illustration which may impress some minds even 
more forcibly than either of those which we have just 
given, is as follows : 

Let us suppose that in some titanic iron-works a steel 
armor-plate had been forged, perfectly circular in shape 
and having a diameter of exactly 185,000,000 miles, or 
very nearly that of the orbit of the earth, and a thickness 
of 8000 miles, or about that of the diameter of the earth. 
Let us further assume that, owing to the attraction of some 
immense stellar body, this huge mass has what we would 
call a weight corresponding to that which a plate of the 
same material would have at the surface of the earth, and 
let it be required to calculate the length of the side of a 
square plate of the same material and thickness and which 
shall be exactly equal to the circular plate. 

Using the 707 places of figures of Mr. Shanks, the length 
of the required side could be calculated so accurately that 
the difference in weight between the two plates (the circle 
and the square) would not be sufficient to turn the scale of 
the most delicate chemical balance ever constructed. 

Of course in assuming the necessary conditions, we are 
obliged to leave out of consideration all those more refined 
details which would embarrass us in similar calculations on 
the small scale and confine ourselves to the purely mathe- 


matical aspect of the case ; but the stretch of imagination 
required is not greater than that demanded by many illus- 
trations of the kind. 

So much, then, for what is claimed by the mathemati- 
cians ; and the certainty that their results are correct, as far 
as they go, is shown by the predictions made by astrono- 
mers in regard to the moon's place in the heavens at any 
given time. The error is less than a second of time in 
twenty-seven days, and upon this the sailor depends for a 
knowledge of his position upon the trackless deep. This 
is a practical test upon which merchants are willing to 
stake, and do stake, billions of dollars every day. 

It is now well established that, like the diagonal and 
side of a square, the diameter and circumference of any 
circle are incommensurable quantities. But, as De Morgan 
says, " most of the quadrators are not aware that it has been 
fully demonstrated that no two numbers whatsoever can 
represent the ratio of the diameter to the circumference, 
with perfect accuracy. When, therefore, we are told that 
either 8 to 25 or 64 to 201 is the true ratio, we know that 
it is no such thing, without the necessity of examination. 
The point that is left open, as not fully demonstrated to 
be impossible, is the geometrical quadrature, the determina- 
tion of the circumference by the straight line and circle, 
used as in Euclid." 

But since De Morgan wrote, it has been shown that a 
Euclidean construction is actually impossible. Those who 
desire to examine the question more fully, will find a very 
clear discussion of the subject in Klein's "Famous Problems 
in Elementary Geometry." (Boston, Ginn & Co.) 

There are various geometrical constructions which give 
approximate results that are sufficiently accurate for most 


practical purposes. One of the oldest of these makes the 
ratio 3y to I. Using this ratio we can ascertain the cir- 
cumference of a circle of which the diameter is given by 
the following method : Divide the diameter into 7 equal 
parts by the usual method. Then, having drawn a straight 
line, set off on it three times the diameter and one of the 
sevenths ; the result will give the circumference with an 
error of less than the one twenty-five-hundredth part or 
one twenty-fifth of one per cent. 

If the circumference had been given, the diameter might 
have been found by dividing the circumference into twenty- 
two parts and setting off seven of them. This would give 
the diameter. A more accurate method is as follows : 

Given a circle, of which it is desired to find the length 
of the circumference : Inscribe in the given circle a square, 
and to three times the diameter of the circle add a fifth of 
the side of the square ; the result will differ from the circum- 

t I 

G F. 

Fig. i. 

ference of the circle by less than one-seventeen-thousandth 
part of it. Another method which gives a result accurate 
to the one-seventeen-thousandth part is as follows : 

Let AD, Fig. i, be the diameter of the circle, C the 
center, and CB the radius perpendicular to AD. Continue 
AD and make DE equal to the radius ; then draw BE, and 
in AE, continued, make EF equal to it ; if to this line EF, 


its fifth part FG be added, the whole line AG will be equal 
to the circumference described with the radius CA, within 
one-seventeen-thousandth part. 

The following construction gives even still closer results : 
Given the semi-circle ABC, Fig 2 ; from the extremities 
A and C of its diameter raise two perpendiculars, one of 
them CE, equal to the tangent of 30, and the other AF, 
equal to three times the radius. If the line FE be then 

Fig. 2. 

drawn, it will be equal to the semi-circumference of the 
circle, within one-hundred-thousandth part nearly. This is 
an error of one-thousandth of one per cent, an accuracy 
far greater than any mechanic can attain with the tools 
now in use. 

When we have the length of the circumference and the 
length of the diameter, we can describe a square which 


shall be equal to the area of the circle. The following is 
the method : 

Draw a line ACB, Fig. 3, equal to half the circumference 
and half the diameter together. Bisect this line in O, and 
with O as a center and AO as radius, describe the semi- 
circle ADB. Erect a perpendicular CD, at C, cutting the 
arc in D ; CD is the side of the required square which can 


Fig. 3. 

then be constructed in the usual manner. The explanation 
of this is that CD is a mean proportional between AC 
and CB. 

De Morgan says : "The following method of finding the 
circumference of a circle (taken from a paper by Mr. S. 
Drach in the * Philosophical Magazine,' January, 1863, 
Suppl.), is as accurate as the use of eight fractional places: 
From three diameters deduct eight-thousandths and seven- 
millionths of a diameter ; to the result, add five per cent. 
We have then not quite enough ; but the shortcoming is 
at the rate of about an inch and a sixtieth of an inch in 
14,000 miles." 

For obtaining the side of a square which shall be equal 
in area to a given circle, the empirical method, given by 
Ahmes in the Rhind papyrus 4000 years ago, is very 


simple and sufficiently accurate for many practical purposes. 
The rule is : Cut off one-ninth of the diameter and construct 
a square upon the remainder. 

This makes the ratio 3.16.. and the error does not exceed 
one-third of one per cent. 

There are various mechanical methods of measuring and 
comparing the diameter and the circumference of a circle, 
and some of them give tolerably accurate results. The 
most obvious device and that which was probably the old- 
est, is the use of a cord or ribbon for the curved surface 
and the usual measuring rule for the diameter. With an 
accurately divided rule and a thin metallic ribbon which 
does not stretch, it is possible to determine the ratio to the 
second fractional place, and with a little care and skill the 
third place may be determined quite closely. 

An improvement which was no doubt introduced at a 
very early day is the measuring wheel or circumferentor. 
This is used extensively at the present day by country 
wheelwrights for measuring tires. It consists of a wheel 
fixed in a frame so that it may be rolled along or over any 
surface of which the measurement is desired. 

This may of course be used for measuring the circumfer- 
ence of any circle and comparing it with the diameter. 
De Morgan gives the following instance of its use : A 
squarer, having read that the circular ratio was undeter- 
mined, advertised in a country paper as follows: "I thought 
it very strange that so many great scholars in all ages 
should have failed in finding the true ratio and have been 
determined to try myself." He kept his method secret, 
expecting "to secure the benefit of the discovery," but it 
leaked out that he did it by rolling a twelve-inch disk along 
a straight rail, and his ratio was 64 to 201 or 3.140625 


exactly. As De Morgan says, this is a very creditable piece 
of work ; it is not wrong by i in 3000. 

Skilful machinists are able to measure to the one-five- 
thousandth of an inch ; this, on a two-inch cylinder, would 
give the ratio correct to five places, provided we could 
measure the curved line as accurately as we can the straight 
diameter, but it is difficult to do this by the usual methods. 
Perhaps the most accurate plan would be to use a fine wire 
and wrap it round the cylinder a number of times, after 
which its length could be measured. The result would 
of course require correction for the angle which the wire 
would necessarily make if the ends did not meet squarely 
and also for the diameter of the wire. Very accurate results 
have been obtained by this method in measuring the diam- 
eters of small rods. 

A somewhat original way of finding the area of a circle 
was adopted by one squarer. He took a carefully turned 
metal cylinder and having measured its length with great 
accuracy he adopted the Archimedean method of finding 
its cubical contents, that is to say, he immersed it in water 
and found out how much it displaced. He then had all 
the data required to enable him to calculate the area of the 
circle upon which the cylinder stood. 

Since the straight diameter is easily measured with great 
accuracy, when he had the area he could readily have found 
the circumference by working backward the rule announced 
by Archimedes, viz : that the area of a circle is equal to 
that of a triangle whose base has the same length as the 
circumference and whose altitude is equal to the radius. 

One would almost fancy that amongst circle-squarers 
there prevails an idea that some kind of ban or magical 
prohibition has been laid upon this problem ; that like the 


hidden treasures of the pirates of old it is protected from 
the attacks of ordinary mortals by some spirit or demoniac 
influence, which paralyses the mind of the would-be solver 
and frustrates his efforts. 

It is only on such an hypothesis that we can account 
for the wild attempts of so many men, and the persistence 
with which they cling to obviously erroneous results in the 
face not only of mathematical demonstration, but of prac- 
tical mechanical measurements. For even when working 
in wood it is easy to measure to the half or even the one- 
fourth of the hundredth of an inch, and on a ten-inch circle 
this will bring the circumference to 3.1416 inches, which is 
a corroboration of the orthodox ratio (3.14159) sufficient 
to show that any value which is greater than 3.142 or less 
than 3.141 cannot possibly be correct. 

And in regard to the area the proof is quite as simple. 
It is easy to cut out of sheet metal a circle 10 inches in 
diameter, and a square of 7.85 on the side, or even one- 
thousandth of an inch closer to the standard 7.854. Now 
if the work be done with anything like the accuracy with 
which good machinists work, it will be found that the circle 
and the square will exactly balance each other in weight, 
thus proving in another way the correctness of the accepted 

But although even as early as before the end of the 
eighteenth century, the value of the ratio had been accu- 
rately determined to 1 5 2 places of decimals, the nineteenth 
century abounded in circle-squarers who brought forward 
the most absurd arguments in favor of other values. In 
1836, a French well-sinker named Lacomme, applied to a 
professor of mathematics for information in regard to the 
amount of stone required to pave the circular bottom of a 


well, and was told that it was impossible " to give a correct 
answer, because the exact ratio of the diameter of a circle 
to its circumference had never been determined" ! This 
absolutely true but very unpractical statement by the pro- 
fessor, set the well-sinker to thinking ; he studied mathe- 
matics after a fashion, and announced that he had discovered 
that the circumference was exactly 3! times the length of 
the diameter ! For this discovery (?) he was honored by 
several medals of the first class, bestowed by Parisian 

Even as late as the year 1860, a Mr. James Smith of 
Liverpool, took up this ratio 3^ to I, and published several 
books and pamphlets in which he tried to argue for its 
accuracy. He even sought to bring it before the British 
Association for the Advancement of Science. Professors 
De Morgan and Whewell, and even the famous mathema- 
tician, Sir William Rowan Hamilton, tried to convince 
him of his error, but without success. Professor Whewell's 
demonstration is so neat and so simple that I make no 
apology for giving it here. It is in the form of a letter to 
Mr. Smith : " You may do this : calculate the side of a 
polygon of 24 sides inscribed in a circle. I think you are 
mathematician enough to do this. You will find that if 
the radius of the circle be one, the side of the polygon is 
.264, etc. Now the arc which this side subtends is, accord- 
ing to your proposition, -=.2604, and, therefore, the 

1 2 

chord is greater than its arc, which, you will allow, is 

This must seem, even to a school-boy, to be unanswer- 
able, but it did not faze Mr. Smith, and I doubt if even the 
method which I have suggested previously, viz., that of 


cutting a circle and a square out of the same piece of sheet 
metal and weighing them, would have done so. And yet 
by this method even a common pair of grocer's scales will 
show to any common-sense person the error of Mr. Smith's 
value and the correctness of the accepted ratio. 

Even .a still later instance is found in a writer who, in 
1892, contended in the New York "Tribune" for 3.2 
instead of 3.1416, as the value of the ratio. He an- 
nounces it as the re-discovery of a long lost 'secret, which 
consists in the knowledge of a certain line called "the 
Nicomedean line." This announcement gave rise to con- 
siderable discussion, and even towards the dawn of the 
twentieth century 3.2 had its advocates as against the 
accepted ratio 3.1416. 

Verily the slaves of the mighty wizard, Michael Scott, 
have not yet ceased from their labors ! 


HIS problem became famous because of the halo 
of mythological romance with which it was sur- 
rounded. The story is as follows : 

About the year 430 B.C. the Athenians were 
afflicted by a terrible plague, and as no ordinary means 
seemed to assuage its virulence, they sent a deputation of 
the citizens to consult the oracle of Apollo at Delos, in the 
hope that the god might show them how to get rid of it. 

The answer was that the plague would cease when they 
had doubled the size of the altar of Apollo in the temple 
at Athens. This seemed quite an easy task ; the altar was 
a cube, and they placed beside it another cube of exactly 
the same size. But this did not satisfy the conditions pre- 
scribed by the oracle, and the people were told that the 
altar must consist of one cube, the size of which must be 
exactly twice the size of the original altar. They then 
constructed a cubic altar of which the side or edge was 
twice that of the original, but they were told that the new 
altar was eight times and not twice the size of the original, 
and the god was so enraged that the plague became worse 
than before. 

According to another legend, the reason given for the 
affliction was that the people had devoted themselves to 
pleasure and to sensual enjoyments and pursuits, and had 
neglected the study of philosophy, of which geometry is 



one of the higher departments certainly a very sound 
reason, whatever we may think of the details of the story. 
The people then applied to the mathematicians, and it is 
supposed that their solution was sufficiently near the truth 
to satisfy Apollo, who relented, and the plague disappeared. 

In other words, the leading citizens probably applied 
themselves to the study of sewerage and hygienic condi- 
tions, and Apollo (the Sun) instead of causing disease by 
the festering corruption of the usual filth of cities, especi- 
ally in the East, dried up the superfluous moisture, and 
promoted the health of the inhabitants. 

It is well known that the relation of the area and the 
cubical contents of any figure to the linear dimensions of 
that figure are not so generally understood as we should 
expect in these days when the schoolmaster is supposed 
to be "abroad in the land." At an examination of candi- 
dates for the position of fireman in one of our cities, several 
of the applicants made the mistake of supposing that a 
two-inch pipe and a five-inch pipe were equal to a seven-inch 
pipe, whereas the combined capacities of the two small 
pipes are to the capacity of the large one as 29 to 49. 

This reminds us of a story which Sir Frederick Bram- 
well, the engineer, used to tell of a water company using 
water from a stream flowing through a pipe of a certain 
diameter. The company required more water, and after 
certain negotiations with the owner of the stream, offered 
double the sum if they were allowed a supply through a 
pipe of double the diameter of the one then in use. This 
was accepted by the owner, who evidently was not aware of 
the fact that a pipe of double the diameter would carry 
four times the supply. 

A square whose side is twice the length of another, and 


a circle whose diameter is twice that of another will each 
have an area four times that of the original. And in the 
case of solids : A ball of twice the diameter will weigh 
eight times as much as the original, and a ball of three times 
the diameter will weigh twenty-seven times as much as the 

In attempting to calculate the side of a cube which shall 
have twice the volume of a given cube, we meet the old 
difficulty of incommensurability, and the solution cannot be 
effected geometrically, as it requires the construction of 
two mean proportionals between two given lines. 



HIS problem is not so generally known as that of 
squaring the circle, and consequently it has not 
received so much attention from amateur mathe- 
maticians, though even within little more than a 
year a small book, in which an attempted solution is given, 
has been published. When it is first presented to an un- 
educated reader, whose mind has a mathematical turn, and 
especially to a skilful mechanic, who has not studied theo- 
retical geometry, it is apt to create a smile, because at first 
sight most persons are impressed with an idea of its sim- 
plicity, and the ease with which it may be solved. And 
this is true, even of many persons who have had a fair gen- 
eral education. Those who have studied only what is 
known as "practical geometry" think at once of the ease 
and accuracy with which a right angle, for example, may 
be divided into three equal parts. Thus taking the right 
angle ACB, Fig. 4, which may be set off more easily and 
accurately than any other angle except, perhaps, that of 
60, and knowing that it contains 90, describe an arc 
ADEB, with C for the center and any convenient radius. 
Now every schoolboy who has played with a pair of com- 
passes knows that the radius of a circle will " step " round 
the circumference exactly six times ; it will therefore 
divide the 360 into six equal parts of 60 each. This 
being the case, with the radius CB, and B for a center, 




describe a short arc crossing the arc ADEB in D, and join 
CD. The angle DCB will be 60, and as the angle ACB 
is 90, the angle ACD must be 30, or one-third part of 
the whole. In the same way lay off the angle ACE of 
60, and ECB must be 30, and the remainder DCE must 
also be 30. The angle ACB is therefore easily divided 


Fig. 4. 

into three equal parts, or in other words, it is trisected. 
And with a slight modification of the method, the same 
may be done with an angle of 45, and with some others. 
These however are only special cases, and the very essence 
of a geometrical solution of any problem is that it shall be 
applicable to all cases so that we require a method by 
which any angle may be divided into three equal parts by 
a pure Euclidian construction. The ablest mathematicians 
declare that the problem cannot be solved by such means, 
and De Morgan gives the following reasons for this conclu- 
sion : " The trisector of an angle, if he demand attention 
from any mathematician, is bound to produce from his con- 
struction, an expression for the sine or cosine of the third 
part of any angle, in terms of the sine or cosine of the 
angle itself, obtained by the help of no higher than the 


square root. The mathematician knows that such a thing 
cannot be ; but the trisector virtually says it can be, and 
is bound to produce it to save time. This is the misfortune 
of most of the solvers of the celebrated problems, that they 
have not knowledge enough to present those consequences 
of their results by which they can be easily judged." 

De Morgan gives an account of a " terrific " construc- 
tion by a friend of Dr. Wallich, which he says is "so 
nearly true, that unless the angle be very obtuse, common 
drawing, applied to the construction, will not detect the 
error." But geometry requires absolute accuracy, not a 
mere approximation. 



T is probable that more time, effort, and money 
have been wasted in the search for a perpetual- 
motion machine than have been devoted to at- 
tempts to square the circle or even to find the 
philosopher's stone. And while it has been claimed in 
favor of this delusion that the pursuit of it has given rise 
to valuable discoveries in mechanics and physics, some 
even going so far as to urge that we owe the discovery of 
the great law of the conservation of energy to the sugges- 
tions made by the perpetual-motion seekers, we certainly 
have no evidence to show anything of the kind. Perpetual 
motion was declared to be an impossibility upon purely 
mechanical and mathematical grounds long before the law 
of the conservation of energy was thought of, and it is very 
certain that this delusion had no place in the thoughts of 
Rumford, Black, Davy, Young, Joule, Grove, and others 
when they devoted their attention to the laws governing 
the transformation of energy. Those who pursued such a 
will-o'-the-wisp, were not the men to point the way to any 
scientific discovery. 

The search for a perpetual-motion machine seems to be 
of comparatively modern origin ; we have no record of the 
labors of ancient inventors in this direction, but this may 
be as much because the records have been lost, as because 
attempts were never made. The works of a mechanical 



inventor rarely attracted much attention in ancient times, 
while the mathematical problems were regarded as amongst 
the highest branches of philosophy, and the search for the 
philosopher's stone and the elixir of life appealed alike to 
priest and layman. We have records of attempts made 
4000 years ago to square the circle, and the history of the 
philosopher's stone is lost in the mists of antiquity ; but it 
is not until the eleventh or twelfth century that we find 
any reference to perpetual motion, and it was not until 
the close of the sixteenth and the beginning of the seven- 
teenth century that this problem found a prominent place 
in the writings of the day. 

By perpetual motion is meant a machine which, without 
assistance from any external source except gravity, shall 
continue to go on moving until the parts of which it is 
made are worn out. Some insist that in order to be prop- 
erly entitled to the name of a perpetual-motion machine, 
it must evolve more power than that which is merely re- 
quired to run it, and it is true that almost all those who 
have attempted to solve this problem have avowed this to 
be their object, many going so far as to claim for their 
contrivances the ability to supply unlimited power at no 
cost whatever, except the interest on a small investment, 
and the trifling amount of oil required for lubrication. 
But it is evident that a machine which would of itself 
maintain a regular and constant motion would be of great 
value, even if it did nothing more than move itself. And 
this seems to have been the idea upon which those men 
worked, who had in view the supposed reward offered for 
such an invention as a means for finding the longitude. 
And it is well known that it was the hope of attaining 
such a reward that spurred on very many of those who 
devoted their time and substance to the subject, 


There are several legitimate and successful methods of 
obtaining a practically perpetual motion, provided we are 
allowed to call to our aid some one of the various natural 
sources of power. For example, there are numerous moun- 
tain streams which have never been known to fail, and 
which by means of the simplest kind of a water-wheel 
would give constant motion to any light machinery. Even 
the wind, the emblem of fickleness and inconstancy, may 
be harnessed so that it will furnish power, and it does not 
require very much mechanical ingenuity to provide means 
whereby the surplus power of a strong gale may be stored 
up and kept in reserve for a time of calm. Indeed this 
has frequently been done by the raising of weights, the 
winding up of springs, the pumping of water into storage 
reservoirs and other simple contrivances. 

The variations which are constantly occurring in the 
temperature and the pressure of the atmosphere have also 
been forced into this service. A clock which required no 
winding was exhibited in London towards the latter part 
of the eighteenth century. It was called a perpetual 
motion, and the working power was derived from variations 
in the quantity, and consequently in the weight of the 
mercury, which was forced up into a glass tube closed at 
the upper end and having the lower end immersed in a 
cistern of mercury after the manner of a barometer. It 
was fully described by James Ferguson, whose lectures on 
Mechanics and Natural Philosophy were edited by Sir 
David Brewster. It ran for years without requiring wind- 
ing, and is said to have kept very good time. A similar 
contrivance was employed in a clock which was possessed 
by the Academy of Painting at Paris. It is described in 
Ozanam's work, Vol. II, page 105, of the edition of 1803. 


The changes which are constantly taking place in the . 
temperature of all bodies, and the expansion and contrac- 
tion which these variations produce, afford a very efficient 
power for clocks and small machines. Professor W. W. R. 
Ball tells us that " there was at Paris in the latter half of 
last century a clock which was an ingenious illustration of 
such perpetual motion. The energy, which was stored up 
in it to maintain the motion of the pendulum, was provided 
by the expansion of a silver rod. This expansion was 
caused by the daily rise of temperature, and by means of a 
train of levers it wound up the clock. There was|a dis- 
connecting apparatus, so that the contraction due to\ a fall 
of temperature produced no effect, and there was a similar 
arrangement to prevent overwinding. I believe that a m$ 
of eight or nine degrees Fahrenheit was sufficient to wind v 
up the clock for twenty-four hours." 

Another indirect method of winding a watch is thus 
described by Professor Ball: 

" I have in my possession a watch, known as the Lohr 
patent, which produces the same effect by somewhat differ- 
ent means. Inside the case is a steel weight, and if the 
watch is carried in a pocket this weight rises and falls at 
every step one takes, somewhat after the manner of a 
pedometer. The weight is moved up by the action of the 
person who has it in his pocket, and in falling the weight 
winds up the spring of the watch. On the face is a small 
dial showing the number of hours for which the watch is 
wound up. As soon as the hand of this dial points to fifty- 
six hours, the train of levers which wind up the watch dis- 
connects automatically, so as to prevent overwinding the 
spring, and it reconnects again as soon as the watch has 
run down eight hours. The watch is an excellent time- 
keeper, and a walk of about a couple of miles is sufficient 
to wind it up for twenty-four hours." 


Dr. Hooper, in his "Rational Recreations," has described 
a method of driving a clock by the motion of the tides, and 
it would not be difficult to contrive a very simple arrange- 
ment which would obtain from that source much more 
power than is required for that purpose. Indeed the prob- 
ability is that many persons now living will see the time 
when all our railroads, factories, and lighting plants will be 
operated by the tides of the ocean. It is only a question 
of return for capital, and it is well known that that has 
been falling steadily for years. When the interest on in- 
vestments falls to a point sufficiently low, the tides will be 
harnessed and the greater part of the heat, light, and power 
that we require will be obtained from the immense amount 
of energy that now goes to waste along our coasts. 

Another contrivance by which a seemingly perpetual 
motion may be obtained is the dry pile or column of De Luc. 
The pile consists of a series of disks of gilt and silvered 
paper placed back to back and alternating, all the gilt sides 
facing one way and all the silver sides the other. The so- 
called gilding is really Dutch metal or copper, and the sil- 
ver is tin or zinc, so that the two actually form a voltaic 
couple. Sometimes the paper is slightly moistened with 
a weak solution of molasses to insure a certain degree of 
dampness ; this increases the action, for if the paper be 
artificially dried and kept in a perfectly dry atmosphere, 
the apparatus will not work. A pair of these piles, each 
containing two or three thousand disks the size of a quarter 
of a dollar, may be arranged side by side, vertically, and 
two or three inches apart. At the lower ends they are 
connected by a brass plate, and the upper ends are 
each surmounted by a small metal bell and between these 
bells a gilt ball, suspended by a silk thread, keeps vibrating 


perpetually. Many years ago I made a pair of these col- 
umns which kept a ball in motion for nearly two years, and 
Professor Silliman tells us that " a set of these bells rang 
in Yale College laboratory for six or eight years unceas- 
ingly." How much longer the columns would have con- 
tinued to furnish energy sufficient to cause the balls to 
vibrate, it might be difficult to determine. The amount of 
energy required is exceedingly small, but since the columns 
are really nothing but a voltaic pile, it is very evident that 
after a time they would become exhausted. 

Such a pair of columns, covered with a tall glass shade, 
form a very interesting piece of bric-a-brac, especially if the 
bells have a sweet tone, but the contrivance is of no prac- 
tical use except as embodied in Bohnenberger's electroscope. 

Inventions of this kind might be multiplied indefi- 
nitely, but none of these devices can be called a perpetual 
motion because they all depend for their action upon energy 
derived from external sources other than gravity. * But 
the authors of these inventions are not to be classed with 
the regular perpetual-motion-mongers. The purposes for 
which these arrangements were invented were legitimate, 
and the contrivances answered fully the ends for which 
they were intended. The real perpetual-motion-seekers 
are men of a different stamp, and their schemes readily fall 
into one of these three classes : I. ABSURDITIES, 2. FAL- 
LACIES, 3. FRAUDS. The following is a description of 
the most characteristic machines and apparatus of which 
accounts have been published. 



In this class may be included those inventions which have 
been made or suggested by honest but ignorant persons in 
direct violation of the fundamental principles of mechanics 
and physics. Such inventions if presented to any expert 
mechanic or student of science, would be at once condemned 
as impracticable, but as a general rule, the inventors of these 
absurd contrivances have been so confident of success, that 
they have published descriptions and sketches of them, and 
even gone so far as to take out patents before they have 
tested their inventions by constructing a working machine. 
It is said, that at one time the United States Patent Office 
issued a circular refusal to all applicants for patents of this 
kind, but at present instead of sending such a circular, the 
applicant is quietly requested to furnish a working model 
of his invention and that usually ends the matter. While 
I have no direct information on the subject, I suspect that 
the circular was withdrawn because of the amount of useless 
correspondence, in the shape of foolish replies and argu- 
ments, which it drew forth. To require a working model 
is a reasonable request and one for which the law duly pro- 
vides, and when a successful model is forthcoming, a patent 
will no doubt be granted ; but until that is presented the 
officials of the Patent Office can have no positive informa- 
tion in regard to the practicability of the invention. 

The earliest mechanical device intended to produce per- 
petual motion is that known as the overbalancing wheel. 
This is described in a sketch book of the thirteenth century 
by Wilars de Honecourt, an architect of the period, and 
since then it has been reinvented hundreds of times. In its 
simplest forms it is thus described and figured by Ozanam : 


" Fig. 5 represents a large wheel, the circumference of 
which is furnished, at equal distances, with levers, each 
bearing at its extremity a weight, and movable on a hinge 
so that in one direction they can rest upon the circumfer- 
ence, while on the opposite side, being carried away by the 
weight at the extremity, they are obliged to arrange them- 
selves in the direction of the radius continued. This being 
supposed, it is evident that when the wheel turns in the 
direction ABC, the weights A, B, and C will recede from the 
center; consequently, as they act with more force, they 
will carry the wheel towards that side ; and as a new lever 

Fig. 5. Fig. 6. 

will be thrown out, in proportion as the wheel revolves, it 
thence follows, say they, that the wheel will continue to 
move in the same direction. But notwithstanding the 
specious appearance of this reasoning, experience has 
proved that the machine will not go ; and it may indeed be 
demonstrated that there is a certain position in which the 
center of gravity of all these weights is in the vertical 
plane passing through the point of suspension, and that 
therefore it must stop." 

Another invention of a similar kind is thus described by 
the same author : 

" In a cylindric drum, in perfect equilibrium on its axis, 
are formed channels as seen in Fig. 6, which contain balls 
of lead or a certain quantity of quicksilver. In consequence 
of this disposition, the balls or quicksilver must, on the one 
side, ascend by approaching the center, and on the other 



must roll towards the circumference. The machine ought, 
therefore, to turn incessantly towards that side." 

In his "Course of Lectures on Natural Philosophy," 
Dr. Thomas Young speaks of these contrivances as fol- 
lows : 

" One of the most common fallacies, by which the super- 
ficial projectors of machines for obtaining perpetual motion 
have been deluded, has arisen from imagining that any 

Fig. 7. 

number of weights ascending by a certain path, on one 
side of the center of motion and descending on the other 
at a greater distance, must cause a constant preponderance 
on the side of the descent: for this purpose the weights 
have either been fixed on hinges, which allow them to fall 
over at a certain point, so as to become more distant from 
the center, or made to slide or roll along grooves or planes 
which lead them to a more remote part of the wheel, from 
whence they return as they ascend; but it will appear on 
the inspection of such a machine, that although some of 
the weights are more distant from the center than others, 


yet there is always a proportionately smaller number of 
them on that side on which they have the greatest power, 
so that these circumstances precisely counterbalance each 

He then gives the illustration (Fig. 7), shown on the 
preceding page, of "a wheel supposed to be capable of pro- 
ducing a perpetual motion; the descending balls acting at a 
greater distance from the center, but being fewer in number 
than the ascending. In the model, the balls may be kept 
in their places by a plate of glass covering the wheel." 

A more elaborate arrangement embodying the same idea 
is figured and described by Ozanam. The machine, which 
is shown in Fig. 8, consists of "a kind of wheel formed of 
six or eight arms, proceeding from a center where the axis 
of motion is placed. Each of these arms is furnished with 
a receptacle in the form of a pair of bellows : but those on 
the opposite arms stand in contrary directions, as seen in 


the figure. The movable top of each receptacle has 
affixed to it a weight, which shuts it in one situation and 
opens it in the other. In the last place, the bellows of the 
opposite arms have a communication by means of a canal, 
and one of them is filled with quicksilver. 

" These things being supposed, it is visible that the bel- 
lows on the one side must open, and those on the other 
must shut ; consequently, the mercury will pass from the 
latter into the former, while the contrary will be the case 
on the opposite side." 

Ozanam naively adds : " It might be difficult to point 
out the deficiency of this reasoning ; but those acquainted 
with the true principles of mechanics will not hesitate to 
bet a hundred to one, that the machine, when constructed, 
will not answer the intended purpose." 

That this bet would have been a perfectly safe one must 
be quite evident to any person who has the slightest knowl- 
edge of practical mechanics, and yet the fundamental idea 
which is embodied in this and the other examples which we 
have just given, forms the basis of almost all the attempts 
which have been made to produce a perpetual motion by 
purely mechanical means. 

The hydrostatic paradox by which a few ounces of liquid 
may apparently balance many pounds, or even tons, has 
frequently suggested a form of apparatus designed to secure 
a perpetual motion. Dr. Arnott, in his " Elements of Phy- 
sics," relates the following anecdote : " A projector thought 
that the vessel of his contrivance, represented here (Fig. 9), 
was to solve the renowned problem of the perpetual mo- 
tion. It was goblet-shaped, lessening gradually towards 
the bottom until it became a tube, bent upwards at c and 
pointing with an open extremity into the goblet again. He 



reasoned thus : A pint of water in the goblet a must more 
than counterbalance an ounce which the tube b will con- 
tain, and must, therefore, be constantly pushing the ounce 
forward into the vessel again at a, and keeping up a stream 
or circulation, which will cease only when the water dries 

Fig. 9. 

up. He was confounded when a trial showed him the 
same level in a and in b" 

This suggestion has been adopted over and over again by 
sanguine inventors. Dircks, in his " Perpetuum Mobile," 
tells us that a contrivance, on precisely the same principle, 
was proposed by the Abbe de la Roque, in " Le Journal 
des Sc^avans," Paris, 1686. The instrument was a U tube, 
one leg longer than the other and bent over, so that any 
liquid might drop into the top end of the short leg, which 
he proposed to be made of wax, and the long one of iron. 
Presuming the liquid to be more condensed in the metal 
than the wax tube, it would flow from the end into the wax 
tube and so continue. 


This is a typical case. A man of learning and of high 
position is so confident that his theory is right that he does 
not think it worth while to test it experimentally, but 
rushes into print and immortalizes himself as the author 
of a blunder. It is safe to say that this absurd invention 
will do more to perpetuate his name than all his learning 
and real achievements. And there are others in the same 
predicament circle-squarers who, a quarter of a century 
hence, will be remembered for their errors when all else 
connected with them will be forgotten. 

To every miller whose mill ceased working for want of 
water, the idea has no doubt occurred that if he could only 
pump the water back again and use it a second or a third 
time he might be independent of dry or wet seasons. Of 
course no practical miller was ever so far deluded as to 
attempt to put such a suggestion into practice, but innu- 
merable machines of this kind, and of the most crude 
arrangement, have been sketched and described in maga- 
zines and papers. Figures of wheels driving an ordinary 
pump, which returns to an elevated reservoir the water 
which has driven the wheel, are so common that it is not 
worth while to reproduce any of them. In the following 
attempt, however, which is copied from Bishop Wilkins' 
famous book, "Mathematical Magic" (1648), the well- 
known Archimedean screw is employed instead of a pump, 
and the naivete of the good bishop's description and con- 
clusion are well worth the space they will occupy. 

After an elaborate description of the screw, he says : 
"These things, considered together, it will hence appear 
how a perpetual motion may seem easily contrivable. 
For, if there were but such a waterwheel made on this 
instrument, upon which the stream that is carried up 


may fall in its descent, it would turn the screw round, 
and by that means convey as much water up as is required 
to move it; so that the motion must needs be continual 
since the same weight which in its fall does turn the wheel, 
is, by the turning of the wheel, carried up again. Or, if 
the water, falling upon one wheel, would not be forcible 
enough for this effect, why then there might be two, or 
three, or more, according as the length and elevation of the 
instrument will admit ; by which means the weight of it 
may be so multiplied in the fall that it shall be equivalent 
to twice or thrice that quantity of water which ascends ; 
as may be more plainly discerned by the following diagram 
(Fig. 10): 

"Where the figure LM at the bottom does represent a 
wooden cylinder with helical cavities cut in it, which at AB 
is supposed to be covered over with tin plates, and three 
waterwheels, upon it, HIK; the lower cistern, which 
contains the water, being CD. Now, this cylinder being 
turned round, all the water which from the cistern ascends 
through it, will fall into the vessel at E, and from that 
vessel being conveyed upon the waterwheel H, shall conse- 
quently give a circular motion to the whole screw. Or, if 
this alone should be too weak for the turning of it, then 
the same water which falls from the wheel H, being re- 
ceived into the other vessel F, may from thence again 
descend on the wheel I, by which means the force of it 
will be doubled. And if this be yet insufficient, then "may 
the water, which falls on the second wheel T, be received 
into the other vessel G, and from thence again descend on 
the third wheel at K ; and so for as many other wheels as 
the instrument is capable of. So that besides the greater 
distance of these three streams from the center or axis by 


which they are made so much heavier; and besides that 
the fall of this outward water is forcible and violent, 
whereas the ascent of that within is natural besides all 
this, there is twice as much water to turn the screw as is 
carried up by it. 

Fig. 10. 

"But, on the other side, if all the water falling upon one 
wheel would be able to turn it round, then half of it would 
serve with two wheels, and the rest may be so disposed of 
in the fall as to serve unto some other useful, delightful 


"When I first thought of this invention, I could scarce 
forbear, with Archimedes, to cry out 'Eureka! Eureka!' 
it seeming so infallible a way for the effecting of a per- 
petual motion that nothing could be so much as probably 
objected against it; but, upon trial and experience, I find it 
altogether insufficient for any such purpose, and that for 
these two reasons : 

1 . The water that ascends will not make any considera- 
ble stream in the fall. 

2. This stream, though multiplied, will not be of force 
enough to turn about the screw." 

How well it would have been for many of those inven- 
tors, who supposed that they had discovered a successful 
perpetual motion, if they had only given their contrivances 
a fair and unprejudiced test as did the good old bishop! 

A modification of this device, in which mercury is used 
instead of water, is thus described by a correspondent of 
"The Mechanic's Magazine." (London.) 

"In Fig. n, A is the screw turning on its two pivots 
GG; B is a cistern to be filled above the level of the lower 
aperture of the screw with mercury, which I conceive to be 
preferable to water on many accounts, and principally be- 
cause it does not adhere or evaporate like water; c is a 
reservoir, which, when the screw is turned round, receives 
the mercury which falls from the top ; there is a pipe, which, 
by the force of gravity, conveys the mercury from the 
reservoir c on to (what for want of a better term may be 
called) the float-board E, fixed at right angles to the center 
[axis] of the screw, and furnished at its circumference with 
ridges or floats to intercept the mercury, the moment and 
weight of which will cause the float-board and screw to re- 
volve, until, by the proper inclination of the floats, the 
mercury falls into the receiver F, from whence it again falls 
by its spout into the cistern G, where the constant revolu- 
tion of the screw takes it up again as before." 


He then suggests some difficulties which the ball, seen 
just under the letter E, is intended to overcome, but he 
confesses that he has never tried it, and to any practical 
mechanic it is very obvious that the machine will not work. 

Fig. ii. 

But we give the description in the language of the inventor, 
as a fair type of this class of perpetual-motion machines. 

In the year 1790 a Doctor Schweirs took out a patent 
for a machine in which small metal balls were used instead 
of a liquid, and they were raised by a sort of chain pump 
which delivered them upon the circumference of a large 
wheel, which was thus caused to revolve. It was claimed 
for this invention that it kept going for some months, but 
any mechanic who will examine the Doctor's drawing must 
see that it could not have continued in motion after the 
initial impulse had been expended. 


That property of liquids known as capillary attraction 
has been frequently called to the aid of perpetual-motion 
seekers, and the fact that although water will, in capillary 
tubes and sponges, rise several inches above the general 
level, it will not overflow, has been a startling surprise to 
the would-be inventors. Perhaps the most notable instance 
of a mistake of this kind occurred in the case of the famous 
Sir William Congreve, the inventor of the military rockets 
that bore his name, and the author of certain improvements 
in matches which were called after him. It was thus de- 
scribed and figured in an article which appeared in the 
" Atlas " (London) and was copied into " The Mechanic's 
Magazine" (London) for 1827: 

" The celebrated Boyle entertained an idea that perpetual 
motion might be obtained by means of capillary attraction; 
and, indeed, there seems but little doubt that nature has 
employed this force in many instances to produce this effect. 

" There are many situations in which there is every 
reason to believe that the sources of springs on the tops 
and sides of mountains depend on the accumulation of 
water created at certain elevations by the operation of 
capillary attraction, acting in large masses of porous ma- 
terial, or through laminated substances. These masses 
being saturated, in process of time become the sources of 
springs and the heads of rivers; and thus by an endless 
round of ascending and descending waters, form, on the 
great scale of nature, an incessant cause of perpetual 
motion, in the purest acceptance of the term, and precisely 
on the principle that was contemplated by Boyle. It is 
probable, however, that any imitation of this process on 
the limited scale practicable by human art would not be 
of sufficient magnitude to be effective. Nature, by the 
immensity of her operations, is able to allow for a slowness 
of process which would baffle the attempts of man in any 
direct and simple imitation of her works. Working, there- 
fore, upon the same causes, he finds himself obliged to 
take a more complicated mode to produce the same effect. 



" To amuse the hours of a long confinement from illness, 
Sir William Congreve has recently contrived a scheme of 
perpetual motion, founded on this principle of capillary at- 
traction, which, it is apprehended, will not be subject to 
the general refutation applicable to those plans in which 
the power is supposed to be derived from gravity only. 
Sir William's perpetual motion is as follows: 

" Let ABC, Fig. 12, be three horizontal rollers fixed in 
a frame; aaa, etc., is an endless band of sponge, running 
round these rollers; and bbb, etc., is an endless chain of 
weights, surrounding the band of sponge, and attached 

to it, so that they must move together; every part of this 
band and chain being so accurately uniform in weight that 
the perpendicular side AB will, in all positions of the band 
and chain, be in equilibrium with the hypothenuse AC, on 
the principle of the inclined plane. Now, if the frame in 
which these rollers are fixed be placed in a cistern of water, 
having its lower part immersed therein, so that the water's 
edge cuts the upper part of the rollers BC, then, if the 
weight and quantity of the endless chain be duly propor- 
tioned to the thickness and breadth of the band of sponge, 
the band and chain will, on the water in the cistern being 
brought to the proper level, begin to move round the rollers 
in the direction AB, by the force of capillary attraction, 
and will continue so to move. The process is as follows : 


" On the side AB of the triangle, the weights bbb, etc., 
hanging perpendicularly alongside the band of sponge, the 
band is not compressed by them, and its pores being left 
open, the water at the point x, at which the band meets its 
surface, will rise to a certain height y, above its level, and 
thereby create a load, which load will not exist on the as- 
cending side CA, because on this side the chain of weights 
compresses the band at the water's edge, and squeezes out 
any water that may have previously accumulated in it; so 
that the band rises in a dry state, the weight of the chain 
having been so proportioned to the breadth and thickness 
of the band as to be sufficient to produce this effect. The 
load, therefore, on the descending side AB, not being op- 
posed by any similar load on the ascending side, and the 
equilibrium of the other parts not being disturbed by the 
alternate expansion and compression of the sponge, the 
band will begin to move in the direction AB; and as it 
moves downwards, the accumulation of water will continue 
to rise, and thereby carry on a constant motion, provided 
the load at xy be sufficient to overcome the friction on the 
rollers ABC. 

" Now to ascertain the quantity of this load in any par- 
ticular machine, it must be stated that it is found by ex- 
periment that the water will rise in a fine sponge about an 
inch above its level; if, therefore, the band and sponge be 
one foot thick and six feet broad, the area of its horizontal 
section in contact with the water would be 864 square 
inches, and the weight of the accumulation of water raised 
by the capillary attraction being one inch rise upon 864 
square inches, would be 30 lb., which, it is conceived, would 
be much more than equivalent to the friction of the rollers." 

The article, inspired no doubt by Sir William, then goes 
on to give elaborate reasons for the success of the device, 
but all these are met by the damning fact that the machine 
never worked. Some time afterwards Sir William, at 
considerable expense, published a pamphlet in which he 
explained and defended his views. If he had only had a 
working model made and the thing had continued in motion 


for a few hours, he would have silenced all objectors far 
more quickly and forcibly than he ever could have done 
by any amount of argument. 

And in his case there could have been no excuse for 
his not making a small machine after the plans that he 
published and even patented. He was wealthy and could 
have commanded the services of the best mechanics in 
London, but no working model was ever made. Many in- 
ventors of perpetual-motion machines offer their poverty 
as an excuse for not making a model or working machine. 
Thus Dircks, in his " Perpetuum Mobile " gives an account 
of " a mechanic, a model maker, who had a neat brass 
model of a time-piece, in which were two steel balls A and 
B ; B to fall into a semicircular gallery C, and be car- 
ried to the end D of a straight trough DE ; while A in its 
turn rolls to E, and so on continuously ; only the gallery C 
not being screwed in its place, we are desired to take the 
will for the deed, until twenty shillings be raised to com- 
plete this part of the work ! " 

And Mr. Dircks also quotes from the " Builder" of 
June, 1847 : " This vain delusion, if not still in force, is at 
least as standing a fallacy as ever. Joseph Hutt, a frame- 
work knitter, in the neighborhood of the enlightened town 
of Hinckley, professes to have discovered it [perpetual 
motion] and only wants twenty pounds, as usual, to set it 

The following rather curious arrangement was described 
in "The Mechanic's Magazine" for 1825. 

" I beg leave to offer the prefixed device. The point at 
which, like all the rest, it fails, I confess I did not (as I 
do now) plainly perceive at once, although it is certainly 
very obvious. The original idea was this to enable a 


body which would float in a heavy medium and sink in a 
lighter one, to pass successively through the one to the 
other, the continuation of which would be the end in view. 
To say that valves cannot be made to act as proposed will 
not be to show the rationale (if I may so say) upon which 
the idea is fallacious." 

The figure is supposed to be tubular, and made of glass, 
for the purpose of seeing the action of the balls inside, 
which float or fall as they travel from air through water 
and from water through air. The foot is supposed to be 
placed in water, but it would answer the same purpose if 
the bottom were closed. 

left leg, filled with water from B to A. 2 and 3, valves, 
having in their centers very small projecting valves ; they 
all open upwards. 4, the right leg, containing air from 
A to F. 5 and 6, valves, having very small ones in their 
centers ; they all open downwards. The whole apparatus 
is supposed to be air and water-tight. The round figures 
represent hollow balls, which will sink one-fourth of their 
bulk in water (of course will fall in air) ; the weight there- 
fore of three balls resting upon one ball in water, as at E, 
will just bring its top even with the water's edge ; the 
weight of four balls will sink it under the surface until the 
ball immediately over it is one-fourth its bulk in water, 
when the under ball will escape round the corner at C, 
and begin to ascend. 

"The machine is supposed (in the figure) to be in 
action, and No. 8 (one of the balls) to have just escaped 
round the corner at C, and to be, by its buoyancy, rising 
up to valve No. 3, striking first the small projecting valve 
in the center, which when opened, the large one will be 


raised by the buoyancy of the ball ; because the moment 
the small valve in the center is opened (although only the 
size of a pin's head), No. 2 valve will have taken upon it- 
self to sustain the whole column of water from A to B. 
The said ball (No. 8) having passed through the valve 


No. 3, will, by appropriate weights or spripgs, close ; the 
ball will proceed upwards to the next valve (No. 2), and 
perform the same operation there. Having arrived at A, 
it will float upon the surface three-fourths of its bulk out 
of water. Upon another ball in due course arriving under 
it, it will be lifted quite out of the water, and fall over the 


point D, pass into the right leg (containing air), and fall to 
valve No. 5, strike and open the small valve in its center, 
then open the large one, and pass through ; this valve will 
then, by appropriate weights or springs, close ; the ball will 
roll on through the bent tube (which is made in that form 
to gain time as well as to exhibit motion) to the next valve 
(No. 6), where it will perform the same operation, and 
then, falling upon the four balls at E, force the bottom one 
round the corner at C. This ball will proceed as did No. 
8, and the rest in the same manner successively." 

That an ordinary amateur mechanic should be misled by 
such arguments is perhaps not so surprising, when we re- 
member that the famous John Bernoulli claimed to have 
invented a perpetual motion based on the difference be- 
tween the specific gravities of two liquids. A translation 
of the original Latin may be found in the Encyclopaedia 
Britannica, Vol. XVIII, page 555. Some of the premises 
on which he depends are, however, impossibilities, and 
Professor Chrystal concludes his notice of the invention 
' thus : " One really is at a loss with Bernoulli's wonderful 
theory, whether to admire most the conscientious state- 
ment of the hypothesis, the prim logic of the demonstra- 
tion so carefully cut according to the pattern of the 
ancients or the weighty superstructure built on so frail 
a foundation. Most of our perpetual motions were clearly 
the result of too little learning ; surely this one was the 
product of too much." 

A more simple device was suggested recently by a cor- 
respondent of "Power." He describes it thus : 

The J-shaped tube A, Fig. 14, is open at both ends, 
but tapers at the lower end, as shown. A well-greased 
cotton rope C passes over the wheel B and through the 



small opening of the tube with practically little or no fric- 
tion, and also without leakage. The tube is then filled with 
water. The rope above the line WX balances over the 
pulley, and so does that below the line YZ . The rope in 

Fig. 14. 

the tube between these lines is lifted by the water, while 
the rope on the other side of the pulley between these lines 
is pulled downward by gravity. 

The inventor offers the above suggestion rather as a 
kind of puzzle than as a sober attempt to solve the famous 
problem, and he concludes by asking why it will not work ? 

In addition to the usual resistance or friction offered by 
the air to all motion, there are four drawbacks : 

1. The friction in its bearings of the axle of the wheel B. 

2. The power required to bend and unbend the rope. 

3. The friction of the rope in passing through the water 
from z to x and its tendency to raise a portion of the water 
above the level of the water at x. 


4. The friction at the point y, this last being the most 
serious of all. An " opening of the tube with practically 
little or no friction, and also without leakage " is a mechan- 
ical impossibility. In order to have the joint water-tight, 
the tube must hug the rope very tightly and this would 
make friction enough to prevent any motion. And the 
longer the column of water xz, the greater will be the ten- 
dency to leak, and consequently the tighter must be the 
joint and the greater the friction thereby created. 

A favorite idea with perpetual-motion seekers is the 
utilization of the force of magnetism. Some time prior to 
the year 1579, Joannes Taisnierus wrote a book which is 
now in the British Museum and in which considerable 
space is devoted to " Continual Motions " and to the 
solving of this problem by magnetism. Bishop Wil- 
kins in his " Mathematical Magick " describes one of the 
many devices which have been invented with this end 
in view. He says : " But amongst all these kinds of inven- 
tion, that is most likely, wherein a loadstone is so disposed 
that it shall draw unto it on a reclined plane a bullet of 
steel, which steel as it ascends near to the loadstone, may 
be contrived to fall down through some hole in the plane, 
and so to return unto the place from whence at first it 
began to move ; and, being there, the loadstone will again 
attract it upwards till coming to this hole, it will fall down 
again ; and so the motion shall be perpetual, as may be 
more easily conceivable by this figure (Fig. 15) : 

" Suppose the loadstone to be represented at AB, which, 
though it have not strength enough to attract the bullet 
C directly from the ground, yet may do it by the help of 
the plane EF. Now, when the bullet is come to the top 
of this plane, its own gravity (which is supposed to exceed 



the strength of the loadstone) will make it fall into that 
hole at E; and the force it receives in this fall will carry it 
with such a violence unto the other end of this arch, that 
it will open the passage which is there made for it, and by 
its return will again shut it : so that the bullet (as at the 

Fig- 15- 

first) is in the same place whence it was attracted, and, 
consequently must move perpetually." 

Notwithstanding the positiveness of the "must " at the 
close of his description, it is very obvious to any practical 
mechanic that the machine will not move at all, far less 
move perpetually, and the bishop himself, after carefully 
and conscientiously discussing the objections, comes to the 
same conclusion. He ends by saying : " So that none of 
all these magnetical experiments, which have been as yet 
discovered, are sufficient for the effecting of a perpetual 
motion, though these kind of qualities seem most conduci- 
ble unto it, and perhaps hereafter it may be contrived from 

It has occurred to several would-be inventors of perpet- 
ual motion that if some substance could be found which 
would prevent the passage of the magnetic force, then by 
interposing a plate of this material at the proper moment, 


between the magnet and the piece of iron to be attracted, 
a perpetual motion might be obtained. Several inventors 
have claimed that they had discovered such a non-conduct- 
ing substance, but it is needless to say that their claims 
had no foundation in fact, and if they had discovered anything 
of the kind, it would have required just as much force to 
interpose it as would have been gained by the interposi- 
tion. It has been fully proved that in every case where a 
machine was made to work apparently by the interposition 
of such a material, a fraud was perpetrated and the machine 
was really made to move by means of some concealed 
springs or weights. 

A correspondent of the " Mechanic's Magazine " (Vol. xii, 
London, 1829), gives the following curious design for a 
" Self -moving Railway Carriage." He describes it as a 
machine which, were it possible to make its parts hold to- 
gether unimpaired by rotation or the ravages of time, and 
to give it a path encircling the earth, would assuredly con- 
tinue to roll along in one undeviating course until time 
shall be no more. 

A series of inclined planes are to be erected in such a 
manner that a cone will ascend one (its sides forming an 
acute angle), and being raised to the summit, descend on 
the next (having parallel sides), at the foot of which it 
must rise on a third and fall on a fourth, and so continue 
to do alternately throughout. 

The diagram, Fig. 16, is the section of a carriage A, 
with broad conical wheels a, a y resting on the inclined plane 
b. The entrance to the carriage is from above, and there are 
ample accommodations for goods and passengers. " The 
most singular property of this contrivance is, that its speed 
increases the more it is laden ; and when checked on any 

6 4 


part of the road, it will, when the cause of stoppage is re- 
moved, proceed on its journey by mere power of gravity. 
Its path may be a circular road formed of the inclined 
planes. But to avoid a circuitous route, a double road 
ought to be made. The carriage not having a retrograde 
motion on the inclined planes, a road to set out upon, and 
another to return by, are indispensable." 

Fig. 16. 

How any one could ever imagine that such a contrivance 
would ever continue in motion for even a short time, 
except, perhaps, on the famous decensus averni, must be a 
puzzle to every sane mechanic. I therefore give it as 
a climax to the absurdities which have been proposed in 
sober earnest. As a fitting close, however, to this chapter 
of human folly, I give the following joke from the "Penny 
Magazine," published by the Society for the Diffusion of 
Useful Knowledge. 

" * Father, I have invented a perpetual motion ! ' said a 
little fellow of eight years old. ' It is thus : I would make 
a great wheel, and fix it up like a water-wheel; at the top 
I would hang a great weight, and at the bottom I would 
hang a number of little weights; then the great weight 


would turn the wheel half round and sink to the bottom, 
because it is so heavy: and when the little weights reach 
the top they would sink down, because they are so many; 
and thus the wheel would turn round for ever.' 

The child's fallacy is a type of all the blunders which 
are made on this subject. Follow a projector in his 
description, and if it be not perfectly unintelligible, which 
it often is, it always proves that he expects to find certain 
of his movements alternately strong and weak not 
according to the laws of nature but according to the 
wants of his mechanism. 


Fallacies are distinguished from absurdities on the one 
hand and from frauds on the other, by the fact that with- 
out any intentionally fraudulent contrivances on the part 
of the inventor, they seem to produce results which have 
a tendency to afford to certain enthusiasts a basis of hope 
in the direction of perpetual motion, although usually not 
under that name, for that is always explicitly disclaimed by 
the promoters. 

The most notable instance of this class in recent times 
was the application of liquid air as a source of power, the 
claim having been actually made by some of the advocates 
of this fallacy that a steamship starting from New York 
with 1000 gallons of liquid air, could not only cross the 
Atlantic at full speed but could reach the other side with 
more than 1000 gallons of liquid air on board the power 
required to drive the vessel and to liquefy the surplus air 
being all obtained during the passage by utilizing the 
original quantity of liquid air that had been furnished in 
the first place. 





That this was equivalent to perpetual motion, pure and 
simple, was obvious even to those who were least familiar 
with such subjects, though the idea of calling it perpetual 
motion was sternly repudiated by all concerned the term 
"perpetual motion" having become thoroughly offensive 
to the ears of common-sense people, and consequently 
tending to cast doubt over any enterprise to which it 
might be applied. 

That liquid air is a real and wonderful discovery, and 
that for a certain small range of purposes it will prove 
highly useful, cannot be doubted by those who have seen 
and handled it and are familiar with its properties, but that 
it will ever be successfully used as an economical source 
of mechanical power is, to say the least, very improbable. 
That a small quantity of the liquid is capable of doing an 
enormous amount of work, and that under some conditions 
there is apparently more power developed than was origin- 
ally required to liquefy the air, is undoubtedly true, but 
when a careful quantitative examination is made of the 
outgo and the income of energy, it will be found in this, 
as in every similar case, that instead of a gain there is a 
very decided and serious loss. The correct explanation of 
the fallacy was published in the " Scientific American," by 
the late Dr. Henry Morton, president of the Stevens 
Institute, and the same explanation and exposure were 
made by the writer, nearly fifty years ago, in the case of 
a very similar enterprise. The form of the fallacy in both 
cases is so similar and so interesting that I shall make no 
apology for giving the details. 

About the year 1853 or 1854, two ingenious mechanics 
of Rochester, N. Y., conceived the idea that by using some 
liquid more volatile than water, a great saving might be 


effected in the cost of running an engine. At that time 
gasolene and benzine were unknown in commerce, and the 
same was true in regard to bisulphide of carbon, but as 
the process of manufacturing the latter was simple and the 
sources of supply were cheap and apparently unlimited, they 
adopted that liquid. The name of one of these inventors 
was Hughes and that of the other was Hill, and it would 
seem that each had made the invention independently of 
the other. They had a fierce conflict over the patent, but 
this does not concern us except to this extent, that the 
records of the case may therefore be found in the archives 
of the Patent Office at Washington, D.C. Hughes was 
backed by the wealth of a well-known lawyer of Rochester, 
whose son subsequently occupied a high office in the state 
of New York, and he constructed a beautiful little steam- 
engine and boiler, made of the very finest materials and 
with such skill and accuracy that it gave out a very consid- 
erable amount of power in proportion to its size. The 
source of heat was a series of lamps, fed, I think, with 
lard oil (this was before the days of kerosene), and the ex- 
hibition test consisted in first filling the boiler with water, 
and noting the time that it took to get up a certain steam 
pressure as shown by the gage. After this test, bisulphide 
of carbon was added to the water, and the time and pres- 
sure were noted. The difference was of course remark- 
able, and altogether in favor of the new liquid. The 
exhaust was carried into a vessel of cold water and as bi- 
sulphide of carbon is very easily condensed and very heavy, 
almost the entire quantity used was recovered and used 
over and over again. 

But to the uninstructed onlooker, the most remarkable 
part of the exhibition was when the steam pressure was so 


far lowered that the engine revolved very slowly, and then, 
on a little bisulphide being injected into the boiler, the 
pressure would at once rise, and the engine would work 
with great rapidity. This seemed almost like magic. 

The same experiment was tried on an engine of twelve 
horse-power, and with a like result. When the steam 
pressure had fallen so far that the engine began to move 
quite slowly, a quantity of the bisulphide would be injected 
into the boiler and the pressure would at once rise, the 
engine would move with renewed vigor, and the fly-wheel 
would revolve with startling velocity. All this was seen 
over and over again by myself and others. At that time 
the writer, then quite a young man, had just recovered 
from a very severe illness and was making a living by 
teaching mechanical drawing and making drawings for in- 
ventors and others, and in the course of business he was 
brought into contact with some parties who thought of in- 
vesting in the new and apparently wonderful invention. 
They employed him to examine it and give an opinion as 
to its value. After careful consideration and as thorough 
a calculation as the data then at command would allow, he 
showed his clients that the tests which had been exhibited 
to them proved nothing, and that if a clear proof of the 
value of the invention was to be given, it must be after a 
run of many hours and not of a few minutes, and against 
a properly adjusted load, the amount of which had been 
carefully ascertained. This test was never made, or if 
made the results were not communicated to the prospec- 
tive purchasers ; the negotiations fell through, and the in- 
vention which was to have revolutionized our mechanical 
industries fell into " innocuous desuetude." 

That the inventors were honest I have no doubt. They 


were themselves deceived when they saw the engine start 
off with tremendous velocity as soon as a little bisulphide 
of carbon was injected into the boiler, and they failed to 
see that this spurt, if I may use the expression, was simply 
due to a draft upon capital previously stored up. The 
capacity of bisulphide of carbon for heat is quite low, when 
compared with that of water ; its vaporizing point is also 
much lower and consequently, an ordinary boiler full of 
hot water contains enough heat to vaporize a considerable 
quantity of bisulphide of carbon at a pretty high pressure. 
In even a still greater measure the same is true of liquid 
air, and this was the underlying fallacy in the case of the 
tests made with liquid-air motors. 


But while the inventors of these schemes may have been 
honest, there is another class who deliberately set out to 
perpetrate a fraud. Their machines work, and work well, 
but there is always some concealed source of power, which 
causes them to move. As a general rule, such inventors 
form a company or corporation of unlimited " lie-ability," as 
De Morgan phrases it, and then they proceed by means of 
flaring prospectuses and liberal advertising, to gather in 
the dupes who are attracted by their seductive promises 
of enormous returns for a very small outlay. Perhaps the 
most widely known of these fraudulent schemes of recent 
years was the notorious Keeley motor, the originator of 
which managed to hoodwink a respectable old lady, and to 
draw from her enormous supplies of cash. At his death, 
however, the absolutely fraudulent nature of his contri- 
vances was fully disclosed, and nothing more has been 


heard of his alleged discovery. But, while he lived and 
was able to put forward claims based upon some apparent 
results, he found plenty of fools who accepted the idea that 
there is nothing impossible to science. 

It is true that the Keeley motor was examined by sev- 
eral committees and some very respectable gentlemen acted 
in such a way as to give a seeming endorsement of the 
scheme, but it must not be supposed for an instant that 
any well-educated engineers and scientific men were de- 
ceived by Mr. Keeley's nonsense. The very fact that he 
refused to allow a complete examination of his machine by 
intelligent practical men, ought to have been enough to 
condemn his scheme, for if he had really made the discovery 
which he claimed there would have been no difficulty in 
proving it practically and thoroughly, and then he might 
have formed company after company that would have re- 
warded him with " wealth beyond the dreams of avarice." 

The Keeley motor was not put forward as a perpetual 
motion ; in these days none of these schemes is admitted 
to be a perpetual motion, for that term has now become 
exceedingly offensive and would condemn any invention ; 
but the result is the same in the end, and the whole his- 
tory of perpetual motion is permeated with frauds of this 
kind, some of them having been so simple that they were 
obvious to even the most unskilled observer, while others 
were exceedingly complicated and most ingeniously con- 
cealed. Many years ago a number of these fraudulent per- 
petual-motion machines were manufactured in America 
and sent over to Great Britain for exhibition, and quite a 
lucrative business was done by showing them in various 
towns. But the fraud was soon detected and the British 
police then made it too warm for these swindlers. 


Mr. Dircks, in his " Perpetuum Mobile," has given ac- 
counts of quite a number of these impostures. The fol- 
lowing are some of the most notable : 

M. Poppe of Tubingen tells of a clock made by M. Geiser, 
which was an admirable piece of mechanism and seemed to 
have solved this great problem in an ingenious and simple 
manner, but it deceived only for a time. When thoroughly 
examined inwardly and outwardly, some time after his 
death, it was found that the center props supporting its 
cylinders contained cleverly constructed, hidden clock-work, 
wound up by inserting a key in a small hole under the sec- 

Another case was that of a man named Adams who ex- 
hibited, for eight or nine days, his pretended perpetual 
motion in a town in England and took in the natives . for 
fifty or sixty pounds. Accident, however, led to a discov- 
ery of the imposture. A gentleman, viewing the machine 
took hold of the wheel or trundle and lifted it up a little, 
which probably disengaged the wheels that connected the 
hidden machinery in the plinth, and immediately he heard 
a sound similar to that of a watch when the spring is run- 
ning down. The owner was in great anger and directly 
put the wheel into its proper position, and the machine 
again went around as before. The circumstance was men- 
tioned to an intelligent person who determined to find out 
and expose the imposture. He took with him a friend to 
view the machine and they seated themselves one on each 
side of the table upon which the machine was placed. 
They then took hold of the wheel and trundle and lifted 
them up, there being some play in the pivots. Immedi- 
ately the hidden spring began to run down and they con- 
tinued to hold the machine in spite of the endeavors of 


the owner to prevent them. When the spring had run 
down, they placed the machine again on the table and 
offered the owner fifty pounds if it could then set itself 
going, but notwithstanding his fingering and pushing, it re- 
mained motionless. A constable was sent for, the impostor 
went before a magistrate and there signed a paper confess- 
ing his perpetual motion to be a cheat. 

In the " Mechanic's Magazine," Vol. 46, is an account 
of a perpetual motion, constructed by one Redhoeffer of 
Pennsylvania, which obtained sufficient notoriety to in- 
duce the Legislature to appoint a committee to enquire 
into its merits. The attention of Mr. Lukens was turned 
to the subject, and although the actual moving cause was 
not discovered, yet the deception was so ingeniously imi- 
tated in a machine of similar appearance made by him and 
moved by a spring so well concealed, that the deceiver him- 
self was deceived and Redhoeffer was induced to believe 
that Mr. Lukens had been successful in obtaining a mov- 
ing power in some way in which he himself had failed, 
when he had produced a machine so plausible in appear- 
ance as to deceive the public. 

Instances of a similar kind might be multiplied in- 

The experienced mechanic who reads the descriptions 
here given of the various devices which have been proposed 
for the construction of a perpetual-motion machine must be 
struck with the childish simplicity of the plans which have 
been offered ; and those who will search the pages of the 
mechanical journals of the last century or who will ex- 
amine the two closely printed volumes in which Mr. Dircks 
has collected almost everything- of the kind, will be aston- 
ished at the sameness which prevails amongst the offerings 


of these would-be inventors. Amongst the hundreds, or, 
perhaps, thousands, of contrivances which have been de- 
scribed, there is probably not more than a dozen kinds 
which differ radically from each other ; the same arrange- 
ment having been invented and re-invented over and over 
again. And one of the strange features of the case is that 
successive inventors seem to take no note of the failure of 
those predecessors who have brought forward precisely the 
same combination of parts under a very slightly different 

It is true that we occasionally find a very elaborate and 
apparently complicated machine, but in such cases it will be 
found, on close examination, to owe its apparent complexity 
to a mere multiplication of parts ; no real inventive ingen- 
uity is exhibited in any case. 

Another singular characteristic of almost all those who 
have devoted themselves to the search for a perpetual 
motion is their absolute confidence in the success of the 
plans which they have brought forth. So confident are 
they in the soundness of their views and so sure of the suc- 
cess of their schemes that they do not even take the trouble 
to test their plans but announce them as accomplished 
facts, and publish their sketches and descriptions as if the 
machine was already working without a hitch. Indeed, so 
far was one inventor carried away with this feeling of con- 
fidence in the success of his machine that he no longer 
allowed himself to be troubled with any doubts as to the 
machine's going- but was greatly puzzled as to what means 
he should take to stop it after it had been set in motion ! 

These facts, which are well known to all who have been 
brought into contact with this class of minds, explain many 
otherwise puzzling circumstances and enable us to place 


a proper value on assertions which, if not made so posi- 
tively and by such apparently good authority, would be at 
once condemned as deliberate falsehoods. That falsehood, 
pure and simple, has formed the basis of a good many 
claims of this kind, there can be no doubt, but at the same 
time, it is probable that some of the claimants really de- 
ceived themselves and attributed to causes other than radi- 
cal errors of theory, the fact that their machines would not 
continue to move. 

While many have claimed the actual invention of a per- 
petual motion it is very certain that not one has ever suc- 
ceeded. How, then, are we to explain the statements 
which have been made in regard to Orffyreus and the 
claims of the Marquis of Worcester? For both of these 
men it is claimed that they constructed wheels which were 
capable of moving perpetually and apparently strong testi- 
mony is offered in support of these assertions. 

In the famous " Century of Inventions," published by 
the Marquis in 1663, four years before his death, the cele- 
brated 56th article reads as follows (verbatim et literatim) : 

" To provide and make that all the Weights of the descend- 
ing side of a Wheel shall be perpetually further from the 
Centre, then those of the mounting side, and yet equal in 
number and heft to the one side as the other. A most in- 
credible thing, if not seen, but tried before the late king 
(of blessed memory) in the Tower, by my directions, two 
Extraordinary Embassadors accompanying His Majesty, and 
the Duke of Richmond and Duke Hamilton, with most of 
the Court, attending Him. The Wheel was 14. Foot over, 
and 40. Weights of 50. pounds apiece. Sir William Balfcre, 
then Lieutenant of the Tower, can justifie it, with several 
others. They all saw, that no sooner these great Weights 
passed the Diameter-line of the lower side, but they hung 
a foot further from the Centre, nor no sooner passed the 
Diameter-line of the upper side, but they hung a foot nearer. 
Be pleased to judge the consequence." 


Such is the account given by the Marquis himself, and 
that he exhibited such a wheel at the time and place which 
he names, I have not the least doubt. And that some of 
the weights on one side hung a foot further from the cen- 
ter than did weights on the other side is also no doubt true, 
but, as the judging of the "consequence" is left to our- 
selves we know that after the first impulse given to it had 
been expended, the wheel would simply stand still unless 
kept in motion by some external force. 

Mr. Dircks in his " Life, Times and Scientific Labours 
of the Second Marquis of Worcester," gives an engraving 
of a wheel which complies with all the conditions laid down 
by the Marquis and which is thus described : 

" Let the annexed diagram, Fig. 17, represent a wheel of 
14 feet in diameter, having 40 spokes, seven feet each, and 
with an inner rim coinciding with the periphery, at one 
foot distance all round. Next provide 40 balls or weights, 
hanging in the center of cords or chains two feet long. 
Now, fasten one end of this cord at the top of the center 


spoke C, and the other end of the cord to the next right- 
hand spoke one foot below the upper end, or on the inner 
ring; proceed in like manner with every other spoke in 
succession; and it will be found that, at A, the cord will 
have the position shown outside the wheel; while at B, C, 
and D, it will also take the respective positions, as shown 
on the outside. The result in this case will be, that all 
the weights on the side A, C, D, hang to the great or outer 
circle, while on the side B, C, D, all the weights are sus- 
pended from the lesser or inner circle. And if we reverse 
the motion of the wheel, turning it from the right to the 
left hand, we shall reverse these positions also (the lower 
end of the cord sliding in a groove towards a left-hand 
spoke), but without the wheel having any tendency to move 
of itself." 

But it is quite as likely that the wheel constructed by 
the Marquis was like one of the "overbalancing" wheels 
described at the beginning of this article. 

It is upon this " scantling " that has been based the 
claim that the Marquis really invented a ,perpetual motion, 
but to those who have seen much of inventors of this kind, 
the discrepancy between the suggested claim made by the 
Marquis and what we know must have been the actual 
results, is easily explained. The Marquis felt sure that 
the thing ought to work, and the excuse for its not doing 
so was probably the imperfect manner in which the wheel 
was made. Only put a little better work on it, says the 
inventor, and it will go. 

Caspar Kaltoff, mechanician to the Marquis, probably 
got the wheel up in a hurry so as to exhibit it on the occa- 
sion of the king's visit to the tower. If he only had had a 
little more time he would have made a machine that would 
have worked. (?) I have heard the same excuse under 
almost the same circumstances, scores of times. 

The case of Orffyreus was very different. The real 


name of this inventor was Jean Ernest Elie-Bessler, and he 
is said to have manufactured the name Orffyreus by plac- 
ing his own name between two lines of letters, and picking 
- out alternate letters above and below. He was educated 
for the church, but turned his attention to mechanics and 
became an expert clock maker. His character, as given 
by his contemporaries was fickle, tricky, and irascible. 
Having devised a scheme for perpetual motion he con- 
structed several wheels which he be self-moving. 
The last one which he made was 1 2 feet in diameter and 
14 inches deep, the material being light pine boards, 
covered with waxed cloth to conceal the mechanism. The 
axle was 8 inches thick, thus affording abundant space for 
concealed machinery. 

This wheel was submitted to the Landgrave of Hesse 
who had it placed in a room which was then locked, and 
the lock secured with the Landgrave's own seal. At the 
end of forty days it was found to be still running. 

Professor 'sGravesande having been employed by the 
Landgrave to make an examination and pronounce upon 
its merits, he endeavored to perform his work thoroughly ; 
this so irritated Orffyreus that the latter broke the machine 
in pieces, and left on the wall a writing stating that he had 
been driven to do this by the impertinent curiosity of the 
Professor ! 

I have no doubt that this was a clear case of fraud, and 
that the wheel was driven by some mechanism concealed 
in the huge axle. As already stated, Orffyreus was at 
one time a clock maker ; now clocks have been made to go 
for a whole year without having to be rewound, so that 
forty days was not a very long time for the apparatus to 
keep in motion. 


Professor 'sGravesande seems to have had some faith 
in the invention, but then we must remember that it would 
not have been very difficult to deceive an honest old pro- 
fessor whose confidence in humanity was probably un- 
bounded. The crowning argument against the genuineness 
of the motion was the fact that the inventor refused to 
allow a thorough examination, although a wealthy patron 
stood ready with a large reward if the machine could be 
proved to be what was claimed. 

And now comes up the question which has arisen in 
regard to other problems, and will recur again and again 
to the end of the chapter : Is a perpetual motion machine 
one of the scientific impossibilities ? 

The answer to this question lies in the fact that there 
is no principle more thoroughly established than that no 
combination of machinery can create energy. So far as 
our present knowledge of nature goes we might as well 
try to create matter as to create energy, and the creation 
of energy is essential to the successful working of a per- 
petual-motion machine because some power must always 
be lost through friction and other resistances and must be 
supplied from some source if the machine is to keep on 
moving. And since the law of the conservation of energy 
makes it positive that no more power can be given out by 
a machine than was originally supplied to it, it seems as 
certain as anything can be that the construction of a per- 
petual-motion machine is one of the impossibilities. 


HE "accursed thirst for gold" has existed from 
the earliest ages and, as the apostle says, " is the 
root of all evil." Those who have a greed for 
power, a craving for luxury, or a fever for lust, 
all think that their wildest dreams might be realized if 
they could only command sufficient gold. Never was 
there a more lurid picture of a mind inflamed with all these 
evil passions than that set forth by Ben Jonson in the 
Second Act of " The Alchemist," and who can doubt but 
that such desires and dreams spurred on many, either to 
engage in an actual search for the philosopher's stone, or 
to become the dupes of what Van Helmont calls " a dia- 
bolical crew of gold and silver sucking flies and leeches." 

As we might naturally expect, the early history of 
alchemy is shrouded in myths and fables. Zosimus the 
Panapolite tells us that the art of Alchemy was first 
taught to mankind by demons, who fell in love with the 
daughters of men, and, as a reward for their favors, taught 
them all the works and mysteries of nature. On this 
Boerhaave remarks : 

" This ancient fiction took its rise from a mistaken in- 
terpretation of the words of Moses, * That the sons of God 
saw the daughters of men that they were fair, and they 
took them wives of all which they chose.' 1 From whence 
it was inferred that the sons of God were daemons, con- 
sisting of a soul, and a visible but impalpable body, like 
1 Genesis vi, 2. 


the image in a looking-glass (to which notion we find 
several allusions in the evangelists); that they know all 
things, appeared to men and conversed with them, fell 
in love with women, had intrigues with them and revealed 
secrets. From the same fable probably arose that of the 
Sibyl, who is said to have obtained of Apollo the gift of 
prophecy, and revealing the will of heaven in return for 
a like favor. So prone is the roving mind of man to fig- 
ments, which it can at first idly amuse itself with, and at 
length fall down and worship." 

This idea of the supernatural origin of the arts perme- 
ates the ancient mythology which everywhere teaches that 
men were taught the sacred arts of medicine and chemis- 
try by gods and demigods. 

Modern science discards all these mythological accounts. 
Whatever knowledge the ancients acquired of medicine and 
chemistry was, no doubt, reached along two lines phar- 
macy and metallurgy. That the pharmacist or apothecary 
exercised his calling at a very early period we have posi- 
tive knowledge ; thus in the Book of Ecclesiastes we are 
told that " dead flies cause the ointment of the apothecary 
to send forth a stinking savor," and that men at a very 
early day found out the means of working iron, copper, 
gold, silver, etc., is evident from the accounts given of 
Vulcan and Tubalcain, as well as from the remains of old 
tools and weapons. And that Alchemy, as it is generally 
understood, is a comparatively modern outgrowth of these 
two arts, is pretty certain. No mention of the art of con- 
verting the baser metals into gold, and no account of a 
universal medicine or elixir of life is to be found in any of 
the authentic writings of the ancients. Homer, Aristotle, 
and even Pliny are all silent on the subject, and those 
writings which treat of the art, and which claim an ancient 
origin, such as the books of Hermes Trismegistus, are now 


regarded by the best authorities as spurious the evi- 
dence that they were the work of a far later age being 

Several writers have taken the ground that the alchemi- 
cal treatises which have come down to us from the early 
writers on the subject, are purely allegorical and do not 
relate to material things, but to the principles of a higher 
religion which, in those days, it was dangerous to expound 
in plain language. One or two elaborate works and several 
articles supporting this view have been published, but the 
common-sense reader who will glance through the im- 
mense collection of alchemical tracts gathered together by 
Mangetus in two folio volumes of a thousand pages each, 
will rise from such examination, very thoroughly convinced 
that it was the actual metal gold, and the fabled universal 
medicine that these writers had in view. 

There can be little doubt that Geber, Roger Bacon, 
Albertus Magnus, Raymond Lully, Helvetius, Van Hel- 
mont, Basil Valentine, and others, describe very substan- 
tial things with a minuteness of detail which leaves no 
room for doubt as to their materiality though we cannot 
always be sure of their identity. 

Some confusion of thought has been caused by the 
difference which has been made between the terms alchemy 
and chemistry and their applications. The word alcJiemy 
is simply the word chemistry with the Arabic word al, 
which signifies the, prefixed, and the history of alchemy is 
really the history of chemistry wild and erratic in its 
beginnings, and giving rise to strange hopes and still 
stranger theories, but ever working along the line of dis- 
covery and progress. And, although many of the profes- 
sional chemists or alchemists of the middle ages were 


undoubted charlatans and quacks, yet did we not have 
many of the same kind in the nineteenth century ? We 
may use the word alchemist as a term of reproach, and apply 
it to these early workers because their theories appear 
to us to be absurd, but how do we know that the chemists 
of the twenty-second century will not regard us in a similar 
light, and set at naught the theories we so fondly cherish ? 

Only seven out of the large number of metals now cata- 
logued by us were known to the ancients ; these were 
gold, silver, mercury, copper, tin, lead, and iron. And as it 
happened that the list of so-called planets also numbered 
exactly seven, it was thought that there must be a connec- 
tion between the two, and, consequently, in the alchemical 
writings, each metal was called by the name of that one of 
the heavenly bodies which was supposed to be connected 
with it in influence and quality. 

In the astronomy of the ancients, as is generally known, 
the earth occupied the center of the universe, and the list 
of planets included the sun and moon. After them came 
Mercury, Venus, Mars, Jupiter, and Saturn. To the metal 
gold was given the name of Sol, or the sun, on account 
of its brightness and its power of resisting corroding agents ; 
hence the compounds of gold were known as solar compounds 
and solar medicines. As might have been expected, silver 
was assigned to Luna or the moon, and in the modern 
pharmacopoeia such terms as lunar caustic and lunar salts 
still have a place. Mercury was, of course, appropriated to 
the planet of that name. Copper was named after Venus, 
and cupreous salts were known as venereal salts. Iron, 
probably from its being the metal chiefly used for making 
arms and armor, was dedicated to Mars, and we still speak 
of martial salts. Tin was named after Jupiter from his bril- 


liancy, the compounds of tin being called jovial salts. The 
dull, leaden color of Saturn, with his apparently heavy and 
slow motion, seemed to fit him for association with lead, and 
we still have the saturnine ointment as a reminder of old 
alchemical times. 

Of these metals gold was supposed to be the only one 
that was perfect, and the belief was general that if the 
others could be purified and perfected they would be 
changed to gold. Many of the old chemists worked faith- 
fully and honestly to accomplish this, but the path to wealth 
seemed so direct and the means for deception were so 
ready and simple, that large numbers of quacks and charla- 
tans entered the field and held out the most alluring induce- 
ments to dupes who furnished them liberally with money 
and other necessaries in the hope that when the discovery 
was made they would be put in possession of unbounded 
wealth. These dupes were easily deceived and led astray 
by simple frauds, which scarcely rose to the level of amateur 
legerdemain. In the " Memoirs of the Academy of 
Sciences" for 1772, M. Geoffroy gives an account of the 
various modes in which the frauds of these swindlers were 
carried on. The following are a few of their tricks : 
Instead of the mineral substances which they pretended 
to transmute they put a salt of gold or silver at the bottom 
of the crucible, the mixture being covered with some pow- 
dered crucible and gum water or wax so that it might 
look like the bottom of the crucible. Another method was 
to bore a hole in a piece of charcoal, fill the hole with fine 
filings of gold or silver, stopping it with powered charcoal, 
mixed with some agglutinent so that the whole might look 
natural. Then when the charcoal burned away, the silver 
or gold was found in the bottom of the crucible. Or they 


soaked charcoal in a solution of these metals and threw 
the charcoal, when powdered, upon the material to be trans- 
muted. Sometimes they whitened gold with mercury and 
made it pass for silver or tin, and the gold when melted was 
exhibited as the result of transmutation. A common ex- 
hibition was to dip nails in a liquid and to take them out 
apparently half converted into gold ; these nails consisted 
of one-half iron neatly soldered to the other half, which was 
gold, and covered with something to conceal the color. 
The paint or covering was removed by the liquid. A very 
common trick was the use of a hollow, iron stirring rod ; 
the hollow was filled with gold or silver filings, and neatly 
stopped with wax. When used to stir the contents of the 
crucible the wax melted and allowed the gold or silver to 
fall out. 

These frauds were rendered all the more easy because 
of certain statements which were current in regard to suc- 
cessful attempts to convert lead and other metals into gold. 
These accounts were vouched for by well-known chemists 
and others of high standing. Perhaps the most famous of 
these is that given by Helvetius in his " Brief of the Golden 
Calf ; Discovering the Rarest Miracle in Nature ; how by 
the smallest portion of the Philosopher's Stone, a great 
piece of common lead was totally transmuted into the purest 
transplendent gold, at the Hague in 1666." The following 
is Brande's abridgment of this singular account. 

" The 27th day of December, 1666, in the afternoon, 
came a stranger to my house at the Hague, in a plebeick 
habit, of honest gravity and serious authority, of a mean 
stature and a little long face, black hair not at all curled, 
a beardless chin, and about forty-four years (as I guess) of 
age and born in North Holland. After salutation, he be- 
secched me with great reverence to pardon his rude accesses, 


for he was a lover of the Pyrotechnian art, and having 
read my treatise against the sympathetic powder of Sir 
Kenelm Digby, and observed my aoubt about the philo- 
sophic mystery, induced him to ask me if I really was a 
disbeliever as to the existence of an universal medicine 
which would cure all diseases, unless the principal parts 
were perished, or the predestinated time of death come. 
I replied, I never met with an adept, or saw such a medi- 
cine, though I had fervently prayed for it. Then I said, 
* Surely you are a learned physician.' 'No,' said he, 'lam a 
brass-founder, and a lover of chemistry. 1 He then took 
from his bosom-pouch a neat ivory box, and out of it three 
ponderous lumps of stone, each about the bigness of a 
walnut. I greedily saw and handled for a quarter of an 
hour this most noble substance, the value of which might 
be somewhere about twenty tons of gold; and having 
drawn from the owner many rare secrets of its admirable 
effects, I returned him this treasure of treasures with a 
most sorrowful mind, humbly beseeching him to bestow a 
fragment of it upon me in perpetual memory of him, though 
but the size of a coriander seed. ' No, no,' said he, ' that is 
not lawful, though thou wouldest give me as many golden 
ducats as would fill this room; for it would have particular 
consequences, and if fire could be burned of fire, I would 
at this instant rather cast it all into the fiercest flames.' 
He then asked if I had a private chamber whose prospect 
was from the public street; so I presently conducted him 
to my best furnished room backwards, which he entered, 
says Helvetius (in the true spirit of Dutch cleanliness), 
without wiping his shoes, which were full of snow and 
dirt. I now expected he would bestow some great secret 
upon me ; but in vain. He asked for a piece of gold, and 
opening his doublet showed me five pieces of that precious 
metal which he wore upon a green riband, and which very 
much excelled mine in flexibility and color, each being 
the size of a small trencher. I now earnestly again craved 
a crumb of the stone, and at last, out of his philosophical 
commiseration, he gave me a morsel as large as a rape- 
seed ; but I said, * This scanty portion will scarcely trans- 
mute four grains of lead.' 'Then,' said he, 'Deliver it me 
back : ' which I did, in hopes of a greater parcel ; but lie, 
cutting off half with his nail, said : ' Even this is sufficient 


for thee.' * Sir,' said I, with a dejected countenance, * what 
means this ? ' And he said, * Even that will transmute half 
an ounce of lead.' So I gave him great thanks, and said I 
would try it, and reveal it to no one. He then took his 
leave, and said he would call again next morning at nine. 
I then confessed, that while the mass of his medicine was 
in my hand the day before, I had secretly scraped off a 
bit with my nail, which I projected on lead, but it caused no 
transmutation, for the whole flew away in fumes. ' Friend,' 
said he, * thou art more dexterous in committing theft than 
in applying medicine ; hadst thou wrapt up thy stolen prey 
in yellow wax, it would have penetrated and transmuted 
the lead into gold.' I then asked if the philosophic work 
cost much or required long time, for philosophers say that 
nine or ten months are required for it. He answered, 
'Their writings are only to be understood by the adepts, 
without whom no student can prepare this magistery. Fling 
not away, therefore, thy money and goods in hunting out 
this art, for thou shalt never find it.' To which I replied, 
' As thy master showed it thee so mayest thou perchance 
discover something thereof to me who know the rudiments, 
and therefore, it may be easier to add to a foundation than 
begin anew.' ' In this art,' said he, ' it is quite otherwise, 
for unless thou knowest the thing from head to heel, thou 
canst not break open the glassy seal of Hermes. But 
enough; tomorrow at the ninth hour I will show thee the 
manner of projection.' But Elias never came again; so 
my wife, who was curious in the art whereof the worthy 
man had discoursed, teazed me to make the experiment 
with the little spark of bounty the artist had left me; so 
I melted half an ounce of lead, upon which my wife put 
in the said medicine ; it hissed and bubbled, and in a quarter 
of an hour the mass of lead was transmuted into fine gold, 
at which we were exceedingly amazed. I took it to the 
goldsmith, who judged it most excellent, and willingly 
offered fifty florins for each ounce." 

Such is the celebrated history of Elias the artist and 
Dr. Helvetius. 

Helvetius stood very high as a man and chemist, but in 
connection with this and some other narratives of the same 


kind, it may be well to remember that something over a 
hundred years before that time the celebrated Paracelsus 
had introduced laudanum. 

The following is another history of transmutation, given 
by Man get us, on the authority of M. Gros, a clergyman of 
Geneva, "of the most unexceptionable character, and at 
the same time a skilful physician and expert chemist." 

" About the year 1650 an unknown Italian came to 
Geneva and took lodgings at the sign of the Green Cross. 
After remaining there a day or two, he requested De Luc, 
the landlord, to procure him a man acquainted with Italian, 
to accompany him through the town and point out those 
things which deserved to be examined. De Luc was ac- 
quainted with M. Gros, at that time about twenty years of 
age, and a student in Geneva, and knowing his proficiency 
in the Italian language, requested him to accompany the 
stranger. To this proposition he willingly acceded, and 
attended the Italian everywhere for the space of a fort- 
night. The stranger now began to complain of want of 
money, which alarmed M. Gros not a little, for at that 
time he was very poor, and he became apprehensive, from 
the tenor of the stranger's conversation, that he intended 
to ask the loan of money from him. But instead of this, 
the Italian asked him if he was acquainted with any gold- 
smith, whose bellows and other utensils they might be 
permitted to use, and who would not refuse to supply them 
with the different articles requisite for a particular process 
which he wanted to perform. M. Gros named a M. Bureau, 
to whom the Italian immediately repaired. He readily 
furnished crucibles, pure tin, quicksilver, and the other 
things required by the Italian. The goldsmith left his 
workshop, that the Italian might be under the less restraint, 
leaving M. Gros, with one of his own workmen as an attend- 
ant. The Italian put a quantity of tin into one crucible, 
and a quantity of quicksilver into another. The tin was 
melted in the fire and the mercury heated. It was then 
poured into the melted tin, and at the same time a red 
powder enclosed in wax was projected into the amalgam. 
An agitation took place and a great deal of smoke was 


exhaled from the crucible ; but this speedily subsided, and 
the whole being poured out, formed six heavy ingots, 
having the color of gold. The goldsmith was called in by 
the Italian and requested to make a rigid examination of 
the smallest of these ingots. The goldsmith not content 
with the touch-stone and the application of aquafortis, 
exposed the metal on the cupel with lead and fused it with 
antimony, but it sustained no loss. He found it possessed 
of the ductility and specific gravity of gold; and full of 
admiration, he exclaimed that he had never worked before 
upon gold so perfectly pure. The Italian made him a 
present of the smallest ingot as a recompense and then, 
accompanied by M. Gros, he repaired to the mint, where 
he received from M. Bacuet, the mint-master, a quantity 
of Spanish gold coin, equal in weight to the ingots which 
he had brought. To M. Gros he made a present of twenty 
pieces on account of the attention that he had paid to him 
and after paying his bill at the inn, he added fifteen pieces 
more, to serve to entertain M. Gros and M. Bureau for 
soms days, and in the meantime he ordered a supper, that 
he might, on his return, have the pleasure of supping with 
these two gentlemen. He went out, but never returned, 
leaving behind him the greatest regret and admiration. 
It is needless to add that M. Gros and M. Bureau continued 
to enjoy themselves at the inn till the fifteen pieces which 
the stranger had left, were exhausted." 

Narratives such as these led even Bergman, a very able 
chemist of the period, to take the ground that " although 
most of these relations are deceptive and many uncertain, 
some bear such character and testimony that, unless we re- 
ject all historical evidence, we must allow them entitled to 

A much more probable explanation is that the relators 
were either dreaming or deceived by clever legerdemain. 

Of the possibility or impossibility of converting the more 
common metals into gold or silver, it would be rash to 
give a positive opinion. To say that gold, silver, lead, 


copper, etc., are elements and cannot be changed, is merely 
to say that we have not been able to decompose them. 
Water, potash, soda, and other substances, were at one 
time considered elements, and resisted all the efforts of 
the older chemists to resolve them into their components, 
but with the advent of more powerful means of analysis 
they were shown to be compounds, and it is not impossible 
that the so-called elements into which they were resolved 
may themselves be found to be compounds. This has 
happened in regard to some substances which were at one 
time announced as elements, and it is not impossible that 
it may happen in regard to others. The ablest chemists 
of the present day recognize this fully and are prepared 
for radical changes in our knowledge of the nature and 
constitution of matter. Amongst the new views is the 
hypothesis of Rutherford and Soddy, which, as given by 
Sir William Ramsay, in a recent article contributed by him 
to " Harper's Magazine," is that, 

" atoms of elements of high atomic weight, such as radium, 
uranium, thorium, and the suspected elements polonium 
and actinium, are unstable ; that they undergo spontaneous 
change into other forms of matter, themselves radioactive 
and themselves unstable; and that finally elements are 
produced, which, on account of their non-radioactivity, are 
as a rule, impossible to recognize, for their minute amount 
precludes the application of any ordinary test with success. 
Tie recognition of helium however, which is compara- 
tively easy of detection, lends great support to this hypo- 

At the same time we must not lose sight of the fact 
that the substances which we now recognize as elements 
have not only resisted the most powerful analytical agencies 
and dissociating forces, but have maintained their ele- 


mental character in spectrum analysis, and shown their 
presence as distinct elements in the sun and other heavenly 
bodies where they must have been subjected to the action 
of the most energetic decomposing forces. So that in the 
present state of our knowledge the near prospect of suc- 
cessful transmutation does not seem to be very bright, 
although we cannot regard it as impossible. In the article 
from which we have already quoted, Sir William Ramsay, 
after discussing the bearing of certain experiments in re- 
gard to the parting with and absorbing of energy by cer- 
tain elements, says: "If these hypotheses are just, then 
the transmutation of the elements no longer appears an 
idle dream. The philosopher's stone will have been dis- 
covered, and it is not beyond the bounds of possibility that 
it may lead to that other goal of the philosophers of the 
dark ages the elixir vitce. ' For the action of living cells 
is also dependent on the nature and direction of the energy 
which they contain ; and who can say that it will be im- 
possible to control their action, when the means of impart- 
ing and controlling energy shall have been investigated ! " 

In the event of the discovery of a cheap method of pro- 
ducing gold, the change which would certainly occur in our 
financial or currency system would be important, if not 
revolutionary. It has become the fashion at present with 
certain writers to scout the so-called "quantitative theory" 
of money as if it were an exposed fallacy. Now the quan- 
titative theory of money rests on one of the most well- 
grounded and firmly established principles in political econ- 
omy : the trouble is that the writers in question do not 
understand it or even know what it is. At present, the 
production of gold barely keeps pace with the increasing 
demand for the metal as currency and in the arts, but if 


that production were increased ten-fold, the value of gold 
would decline and prices would go up astonishingly. 

One of the objects which the better class of alchemists 
had in view was the making of gold to such an extent that 
it might become quite common and cease to be sought after 
by mankind. One alchemical writer says : " Would to 
God that all men might become adepts in our art, for then 
gold, the common idol of mankind, would lose its value and 
we should prize it only for its scientific teaching." 



HIS is really one of the processes supposed to 
be involved in the transmutation of the metals 
and might, therefore, perhaps, with propriety, be 
included under that head. But as it has received 
special attention in the apocryphal works of Hermes Tris- 
megistus, who is generally regarded as the Father of Al- 
chemy, it is frequently mentioned as one of the old scientific 
problems. Readers of Scott's novel, " Kenilworth," may 
remember that Wayland Smith, in his account of his former 
master, Demetrius Doboobius, describes him as a profound 
chemist who had " made several efforts to fix mercury, and 
judged himself to have made a fair hit at the philosopher's 
stone." Hermes, or, rather, those who wrote over his 
name, speaks in the jargon of the adepts, about " catching 
the flying bird," by which is meant mercury, and "drown- 
ing it so that it may fly no more." The usual means for 
effecting this was amalgamation with gold, or some other 
metal or solution in some acid. 

To the ancient chemists mercury must have been one of 
the most interesting of objects. Its great heaviness, its 
metallic brilliancy, and its wonderful mobility, must all have 
combined to render it a subject for deep thought and an 
attractive object for experiment and investigation. 

Living in a warm climate, as they did, there was no 
means at their command by which its fluidity could be im- 
paired. This subtle substance seemed to defy the usual 



attempts to grasp it ; it rolled about like a solid sphere, but 
offered no resistance to the touch, and when pressed it split 
up into innumerable smaller globules so that the problem 
of " fixing " it must have had a strange fascination for the 
thoughtful alchemist, especially when he found that, on 
subjection to a comparatively moderate degree of heat, this 
heavy metal disappeared in vapor and left not a trace behind. 

I have often wondered what the old alchemists would 
have said if they had seen fluid mercury immersed in a 
clear liquid and brought out in the form of a lump of solid, 
bright metal. For, although this is not in any sense a so- 
lution of the problem, yet it is a most curious sight and one 
which was rarely seen before the discovery of the liquefac- 
tion of the gases. To Geber, Basil Valentine, Van Helmont, 
Helvetius, and men of their day, living in their climate, this 
startling phenomenon would have seemed nothing short of 
a miracle. 

In modern times the solidification of mercury had been 
frequently witnessed by these who dwelt in northern cli- 
mates and by the skilful use of certain freezing mixtures 
made up of ordinary salts, it is not difficult to exhibit this 
metal in the solid state at any time. But it was not until the 
discovery of the liquefaction of carbonic acid, nitrous oxide, 
and other gases by Faraday, about 1823, that the freezing 
of mercury became a common lecture-room experiment. 

In the year 1 862 the writer delivered a course of lectures 
on chemistry, in the city of Rochester, N. Y., and during 
the progress of these lectures he reduced carbonic acid first 
to the liquid, and then to the solid state, in the form of a 
white snow. The temperature of this snow was about 
80 Cent. ( 1 76 Fahr.) and when it was mixed with 
ether and laid on a quantity of mercury, the latter was 


quickly frozen. In this way it was easy to make a ham- 
mer-head of frozen mercury and drive a nail with it. 

Another very interesting experiment was the freezing of 
a slender triangular bar of mercury which might be twisted, 
bent, and tied in a knot. This was done by folding a long 
strip of very stiff paper so as to make an angular trough 
into which the mercury was poured. This trough was then 
carefully leveled and a mixture of solid carbonic acid and 
ether was placed over the metal in the usual way. In a few 
seconds the mercury was frozen quite solid so that it could 
be lifted out by means of two pairs of wooden forceps and 
bent and knotted at will. But the most striking part of the 
experiment was the melting of this bar of mercury by 
means of a piece of ice. The moment the ice touched the 
mercury, the latter melted and fell down in drops in the 
same way that a bar of lead or solder melts when it is 
touched with a red-hot iron. 

The melted mercury was allowed to fall into a tall ale-glass 
of water, the temperature of which had been reduced as 
nearly as possible to the freezing point. When the mercury 
came in contact with the cold water, the latter began to freeze 
and by careful manipulation it was possible to freeze a tube 
of ice through the center of the column of water. The 
effect of this under proper illumination was very striking. 

Owing to the fact that the specific heat or thermal ca- 
pacity of mercury is only about one-thirtieth of that of 
water, it requires a considerable amount of melted mercury 
to produce the desired result. 

But these processes do not enable us to fix mercury in 
the alchemical sense; the accomplishment of that still 
remains an unsolved problem, and it is more than likely 
that it will remain so, 



OVE of life is a characteristic of all animals, man 
included, and notwithstanding the fact that an 
occasional individual becomes so dissatisfied with 
his environment that he commits suicide, and 
also in the face of the poet's assertion that 

"protracted life is but protracted woe" 

most men and women are of the same way of thinking as 
Charmian, the attendant on Cleopatra, and "love long life 
better than figs." And the force of this general feeling is 
appealed to in the only one of the Mosaic commandments 
to which a promise is attached, the inducement for honor- 
ing father and mother being " that thy days may be long 
in the land that the Lord thy God giveth thee." 

No wonder then that the old alchemists dreamed of a 
universal medicine that would not only prevent or cure 
sickness but that would renew the youth of the aged and 
the feeble, for in this, as in most other attempts at discov- 
ery, the wish was father to the thought. That the renewal 
of youth in the aged was supposed to be within the ability 
of the magicians and gods of old, we gather from the stories 
of Medea and Aeson and the ivory shoulder of Pelops, as 
referred to in Shakespeare, and explained in the " Shake- 
speare Cyclopaedia." 

Of the form of this supposed elixir we know very little 



for the language of the alchemists was so vague and mys- 
tical that it is often very difficult to ascertain their meaning 
with any approach to certainty. The following, which is a 
fair sample of their metaphorical modes of expressing them- 
selves, is found in the works of Geber. In one of his writ- 
ings, he exclaims : " Bring me the six lepers that I may 
cleanse them." Modern commentators explain this as being 
his mode of telling his readers that he would convert into 
gold the six inferior or, as they were called by the alchem- 
ists, the six imperfect metals. No wonder that Dr. John- 
son adopted the idea that the word gibberish (anciently 
written geberisli) owed its origin to an epithet applied to 
the language of Geber and his tribe. 

Some have claimed that the elixir and the philosopher's 
stone were one and the same thing, and some of the writ- 
ings of the old alchemists would seem to confirm this view. 
Thus, at the close of a formula for preparing the philoso- 
pher's stone, Carolus Musitanus gives the following ad- 
monition : 

"Thus friend, you have a description of the universal 
medicine, not only for curing diseases and prolonging life, 
but also for transmuting all metals into gold. Give there- 
fore thanks to Almighty God, who, taking pity on human 
calamities, has at last revealed this inestimable treasure, 
and made it known for the benefit of all." 

And Brande tells us that "nearly all the alchemists 
attributed the power of prolonging life either to the philoso- 
pher's stone or to certain preparations of gold, imagining 
possibly that the permanence of that metal might be trans- 
ferred to the human system. The celebrated Descartes is 
said to have supported such opinions ; he told Sir Kenelm 
Digby that although he would not venture to promise im- 
mortality, he was certain that life might be lengthened to 


the period of that of the Patriarchs. His plan, however, 
seems to have been the very rational one of limiting all 
excess of diet and enjoining punctual and frugal meals." 

It is an old saying that history repeats itself. About 
forty years ago certain medical practitioners strongly urged 
the use of salts of gold in the treatment of disease, and 
great hopes were entertained in regard to their efficacy. 
And the Keeley gold cure for drunkards is strongly in 
evidence, even at the present day. 

On the other hand, some have held that the elixir was 
quite distinct from the stone by which metals might be 
transmuted into gold. In the second part of "King Henry 
IV," Falstaff (Act III, Scene 2, line 355), says of Shallow: 
"it shall go hard but I will make him a philosopher's two 
stones to me," and this saying of his has given considerable 
trouble to the commentators. 

Warburton's explanation of this expression is, that "there 
was two stones, one of which was a universal medicine and 
the other a transmuter of base metals into gold." And in 
Churchyard's " Discourse and Commendation of those that 
can make Gold," we read of Remundus, who 

Wrate sundry vvorkes, as well doth yet appeare 
Of stone for gold, and shewed plaine and cleare 
A stone for health. 

Johnson and some others have objected to this explana- 
tion, but it seems to be evident that Falstaff meant that he 
would get health and wealth from Shallow. He got the 
wealth to the extent of a thousand pounds. 

The intense desire which exists in the human bosom 
for an elixir that will cure all diseases, and prolong life has 
made itself evident, even in recent times, and has called 


forth serious efforts on the part of men occupying promi- 
nent positions in the scientific world. Both in Europe and 
in this country suggestions have been made of fluids which, 
when injected into the veins of the old and the feeble, 
would renew youth and impart fresh strength. But alas ! 
the results thus far attained have been anything but grati- 
fying, and the probabilities against success in this direction 
are very strong. 

The latest gleam of light comes from discoveries in con- 
nection with the radioactive elements, as the reader will find, 
on referring to Sir William Ramsay's utterance, which is 
given at the close of the article on the " Transmutation of 
the Metals," on a preceding page. 


IN addition to the seven " Follies," of which an account 
has been given in the preceding pages, there are a few 
which deserve to be classed with them, although they do 
not find a place in the usual lists. These are known as 






ART of the sepulchral rites of the ancients con- 
sisted in placing lighted lamps in the tombs or 
vaults in which the dead were laid, and, in many 
cases, these lamps were carefully tended and kept 
continually burning. Some authors have claimed, how- 
ever, that these men of old were able to construct lamps 
which burned perpetually and required no attention. In 
number 379 of the " Spectator " there is an anecdote of 
some one having opened the sepulcher of the famous 
Rosicrucius. There he discovered a lamp burning which 
a statue of clock-work struck into pieces. Hence, says the 
writer, the disciples of this visionary claimed that he had 
made use of this method to show that he had re-invented 
the ever-burning lamps of the ancients. And Fortunio 
Liceti wrote a book in which he collected a large number 
of stories about lamps, said to have been found burning in 
tombs or vaults. Ozanam fills eight closely printed pages 
with a discussion of the subject. 

Attempts have been made to explain many of the facts 
upon which is based the claim that the ancients were able 
to construct perpetual lamps by the suggestion that the 
light sometimes seen on the opening of ancient tombs 
may have been due to the phosphorescence which is well 
known to arise during the decomposition of animal and 
vegetable matter. Decaying wood and dead fish are familiar 
objects which give out a light that is sufficient to render 
dimly visible the outlines of surrounding objects, and such 



a light, seen in the vicinity of an old lamp, might give rise 
to the impression that the lamp had been actually burning 
and that it had been blown out by sudden exposure to a 
draft of air. 

Another supposition was that the flame, which was sup- 
posed to have been seen, may have been caused by the 
ignition of gases arising from the decomposition of dead 
bodies, and set on fire by the flambeaux or candles of the 
investigators, and it is quite possible that the occurrence 
of each of these phenomena may have given a certain 
degree of confirmation to preconceived ideas. 

After the discovery of phosphorus in 1669, by Brandt 
and Kunckel, it was employed in the construction of lumin- 
ous phials which could be carried in the pocket, and which 
gave out sufficient light to enable the 'user to see the 
hands of a watch on a dark night. Directions for making 
these luminous phials are very simple, and may be found 
in most of the books of experiments published prior to the 
introduction of the modern lucifer match. They were 
also used for obtaining a light by means of the old matches, 
which were tipped merely with a little sulphur, and which 
could not be ignited by friction. Such a match, after being 
dipped into one of these phosphorus bottles, would readily 
take fire by slight friction, and some persons preferred this 
contrivance to the old flint and steel, partly, no ^doubt, 
because it was a novelty. But these bottles were not in 
any sense perpetual, the light being due to the slow oxida- 
tion of the phosphorus so that, in a comparatively short 
time, the luminosity of the materials ceased. Nevertheless, 
it has been suggested that some form of these old luminous 
phials may have been the original perpetual lamp. 

After the discovery of the phosphorescent qualities of 


barium sulphate or Bolognian phosphorus, as it was called, 
it was thought that this might be a re-discovery of the 
long-lost art of making perpetual lamps. But it is well 
known that this substance loses its phosphorescent power 
after being kept in the dark for some time, and that occa- 
sional exposure to bright sun-light is one of the conditions 
absolutely essential to its giving out any light at all. This 
condition does not exist in a dark tomb. 

A few years ago phosphorescent salts of barium and 
calcium were employed in the manufacture of what was 
known as luminous paint. These materials shine in the 
dark with brilliancy sufficient to enable the observer to 
read words and numbers traced with them, but regular 
exposure to the rays of the sun or some other bright light 
is absolutely necessary to enable them to maintain their 

More recently it has been suggested that the ancients 
may have been acquainted with some form of radio-active 
matter like radium, and that this was the secret of the 
lamps in question. It is far more likely, however, that the 
reports of their perpetual lamps were based upon mere 
errors of observation. 

The perpetual lamp is, in chemistry, the counterpart of 
perpetual motion in mechanics both violate the funda- 
mental principle of the conservation of energy. And just 
as suggestions of impossible movements have been numer- 
ous in the case of perpetual motion, so impossible devices 
and constructions have been suggested in regard to perpet- 
ual lamps. Prior to the development, or even the sugges- 
tion of the law of the conservation of energy, it was believed 
that it might be possible to find a liquid which would burn 
without being consumed, and a wick which would feed the 


liquid to the flame without being itself destroyed. Dr. 
Plott suggested naphtha for the fluid and asbestos for the 
wick, but since kerosene oil, naphtha, gasolene, and other 
liquids of the kind have become common, every housewife 
knows that as her lamp burns, the oil, of whatever kind it 
may be, disappears. 

Under present conditions the construction of a perpetual 
lamp is not a severely felt want ; for constancy and bril- 
liancy our present means of illumination are sufficient for 
almost all our requirements. Whether or not it would be 
possible to gather up those natural currents of electricity, 
which are suspected to flow through and over the earth, and 
utilize them for purposes of illumination, however feeble, 
it might be difficult to decide. But such means of perpet- 
ual electric lighting would be similar to a perpetual motion 
derived from a mountain stream. Such natural means of 
illumination already exist, and have existed for ages in the 
fire-giving wells of naphtha which are found on the shores 
of the Caspian sea, and in other parts of the east, and 
which have long been objects of adoration to the fire- 

As for the outcome of present researches into the prop- 
erties of radium, polonium, and similar substances, and 
their possible applications, it is too early to form even a 


HE production of a universal solvent or alkahest 
was one of the special problems of the alchemists 
in their general search for the philosopher's 
stone and the means of transmuting the so-called 
inferior metals into gold and silver. Their idea of the 
way in which it would aid them to attain these ends does 
not seem to be very clearly stated in any work that I have 
consulted ; probably they thought that a universal solvent 
would wash away all impurities from common materials 
and leave in absolute purity the higher substance, which 
constituted the gold of the adepts. But whatever their 
particular object may have been, it is well known that much 
time and labor were expended in the fruitless search. 

The futility of such attempts was very well exposed by 
the cynical sceptic, who asked them what kind of vessel 
could they provide for holding such a liquid ? If its solvent 
powers are such that it dissolves everything, it is very evi- 
dent that it would dissolve the very material of the vessel 
in which it must be placed. 

When hydrofluoric acid became a subject of investigation 
it was thought that its characteristics approached, more 
nearly than those of any other substance known, to those 
of the universal solvent, and the very difficulty above sug- 
gested, presented itself strongly to the chemists who ex- 
perimented with it. Not only common metals but glass 
and porcelain were acted upon by this wonderfully ener- 
getic liquid and when attempts were made to isolate the 



fluorine, even the platinum electrodes were corroded and 
destroyed. Vessels of pure silver and of lead served toler- 
ably well, but Davy suggested that the most scientific 
method of constructing a containing vessel would be to use 
a compound in which fluorine was already present to the 
point of saturation. As there is a limit to the amount of 
fluorine with which any base can combine, such a vessel 
would be proof against its solvent action. I am not aware, 
however, that the suggestion was ever carried into actual 
practice with success. 


HIS singular delusion may have been partly due 
to errors of observation, the instruments and 
methods of former times having been notably 
crude and unreliable. This fact, taken in con- 
nection with the wild theories upon which the natural 
sciences of the middle ages were based, is a sufficient ex- 
planation of some of the extraordinary statements made by 
Kircher, Schott, Digby, and ethers. 

By palingenesy these writers meant a certain chemical 
process by means of which a plant or an animal might be 
revived from its ashes. In other words a sort of material 
resurrection. Most of the accounts given by the old au- 
thors go no further than to assert that by proper methods 
the ashes of plants, when treated with water, produce small 
forests of ferns and pines. Thus, an English chemist, 
named Coxe, asserts that having extracted and dissolved 
the essential salts of fern, and then filtered the liquor, he 
observed, after leaving it at rest for five or six weeks, a 
vegetation of small ferns adhering to the bottom of the 
vessel. The same chemist, having mixed northern potash 
with an equal quantity of sal ammoniac, saw, some time 
after, a small forest of pines and other trees, with which he 
was not acquainted, rising from the bottom of the vessel. 

And Kircher tells us in his " Ars Magnetica " that he 
had a long-necked phial, hermetically sealed, containing 
the ashes of a plant which he could revive at pleasure by 
means of heat ; and that he showed this wonderful phe- 



nomenon to Christina, Queen of Sweden, who was highly 
delighted with it. Unfortunately he left this valuable 
curiosity one cold day in his window and it was entirely 
destroyed by the frost. Father Schott also asserts that 
he saw this chemical wonder which, according to his ac- 
count, was a rose revived from its ashes. And he adds 
that a certain prince having requested Kircher to make 
him one of the same kind, he chose rather to give up his 
own than to repeat the operation. 

Even the celebrated Boyle, though not very favorable to 
palingenesy, relates that having dissolved in water some 
verdigris, which, as is well known, is produced by combin- 
ing copper with the acid of vinegar, and having caused this 
water to congeal, by means of artificial cold, he observed, at 
the surface of the ice, small figures which had an exact 
resemblance to vines. 

In this connection it is well to bear in mind that in 
Boyle's time almost all vinegar was really what its name 
implies sour wine (vin aigre] and verdegris or copper 
acetate was generally prepared by exposing copper plates 
to the action of refuse grapes which had been allowed to 
ferment and become sour. Therefore to him it might not 
have seemed so very improbable that the green crystals 
which appeared on the surface of the ice were, in reality, 
minute resuscitated grape-vines. 

The explanation of these facts given by Father Kircher 
is worthy of the science of the times. He tells us that 
the seminal virtue of each mixture is contained in its salts 
and these salts, unalterable by their nature, when put in 
motion by heat, rise in the vessel through the liquor in 
which they are diffused. Being then at liberty to arrange 
themselves at pleasure, they place themselves in that order 


in which they would be placed by the effect of vegetation, 
or the same as they occupied before the body to which they 
belonged had been decomposed by the fire ; in short, they 
form a plant, or the phantom of a plant, which has a per- 
fect resemblance to the one destroyed. 

That the operators have here mistaken for true vegetable 
growth the fern-like crystals of the salts which exist in the 
ashes of all plants is very obvious. Their knowledge of 
plant structure was exceedingly limited and their micro- 
scopes were so imperfect that imagination had free scope. 
As seen under our modern microscopes, there are few pret- 
tier sights than the crystallization of such salts as sal 
ammoniac, potassic nitrate, barium chloride, etc. The crys- 
tals are actually seen to grow and it would not require a 
very great stretch of the imagination to convince one that 
the growth is due to a living organism. Indeed, this view 
has actually been taken in an article which recently ap- 
peared in a prominent magazine. The writer of that article 
sees no difference between the mere aggregation of inor- 
ganic particles brought together by voltaic action and the 
building up of vital structures under the influence of or- 
ganic forces. This is simply materialism run mad. 

Perhaps the finest illustration of such crystallization is 
to be found in the deposition of silver from a solution of 
the nitrate as seen under the microscope. A drop of the 
solution is placed on a glass slide and while the observer 
watches it through a low power, a piece of copper wire or, 
preferably, a minute quantity of the amalgam of tin and 
mercury, such as is used for " silvering " cheap looking 
glasses, is brought into contact with it. Chemical decom- 
position at once sets in and then the silver thus deposited 
forms one element of a very minute voltaic couple and 


fresh crystals of silver are deposited upon the silver already 
thrown down. When the illumination of this object under 
the microscope is properly managed, the appearance, which 
resembles that shown in Fig. 18, is exceedingly brilliant, 
and beautiful beyond description. 

That imagination played strange pranks in the observa- 
tions of the older microscopists is shown by some of the 
engravings found in their books. I have now before me a 

Fig. 18. 

thick, dumpy quarto in which the so-called seminal animal- 
cules are depicted as little men and women, and I have no 
doubt that, to the eye of this early observer, they had that 
appearance. But the microscopists of to-day know better. 
Sir Kenelm Digby, whose name is associated with the 
Sympathetic Powder, tells us that he took the ashes of 
burnt crabs, dissolved them in water and, after subjecting 
the whole to a tedious process, small crabs were produced 
in the liquor. These were nourished with blood from the 


ox, and, after a time, left to themselves in some stream 
where they throve and grew large. 

Now, although Evelyn, in his diary, declares that " Sir 
Kenelm was an errant mountebank," it is quite possible that 
he was honest in his account of his experiments and that he 
was merely led astray by the imperfection of his instru- 
ments of observation. It is more than likely that the 
creatures which Digby saw were entomostraca introduced 
in the form of ova which, unless a good microscope be used, 
are quite invisible. These would develop rapidly and might 
easily be mistaken for some species of crab, though, when 
examined with proper instruments, all resemblance vanishes. 
When let loose in a running stream it would evidently be 
impossible to trace their identity and follow their growth. 

But while some of these stories may have originated in 
errors of observation .this will hardly explain some of the 
statements made by those who have advocated this strange 
doctrine. Father Schott, in his "Physica Curiosa," gives 
an account of the resurrection of a sparrow and actually 
gives an engraving in which the bird is shown in a bottle 
revived ! 

Although the subject, of itself, is not worthy of a mo- 
ment's consideration, it deserves attention as an illustration 
of the extraordinary vagaries into which the human mind 
is liable to fall. 


HIS curious occult method of curing wounds is 
indissolubly associated with the name of Sir 
Kenelm Digby (born 1603, died 1665), though 
it was undoubtedly in use long before his time. 
He himself tells us that he learned to make and apply the 
drug from a Carmelite, who had traveled in the east, and 
whom he met in Florence, in 1622. The descendants of 
Digby are still prominent in England, and O. W. Holmes, 
in his " One Hundred Days in Europe," tells us that he 
had met a Sir Kenelm Digby, a descendant of the famous 
Sir Kenelm of the seventeenth century, and that he could 
hardly refrain from asking him if he had any of his ancestor's 
famous powder in his pocket. 

Digby was a student of chemistry, or at least of the 
chemistry of those days, and wrote books of Recipes and 
the making of " Methington [metheglin or mead ?] Syder, 
etc." He was, as we have seen in the previous article, 
a believer in palingenesy and made experiments with a view 
to substantiate that strange doctrine. Evelyn calls him an 
"errant quack," and he may have been given to quackery, 
but then the loose scientific ideas of those days allowed a 
wide range in drawing conclusions which, though they seem 
absurd to us, may have appeared to be quite reasonable to 
the men of that time. 

From his book on the subject, 1 we learn that the wound 

1 Touching the Cure of Wounds by the Powder of Sympathy. With 
Instructions how to make the said Powder. Rendered faithfully out of 
French into English by R. White, Gent. London, 1658. 



was never to be brought into contact with the powder. A 
bandage was to be taken from the wound, immersed in the 
powder, and kept there until the wound healed. 

This beats the absent treatment of Christian Science ! 

The powder was simply pulverized vitriol, that is, ferric 
sulphate, or sulphate of iron. 

There was another and probably an older method of 
using sympathetic powders and salves ; this was to apply 
the supposed curative to the weapon which caused the 
wound, instead of the wound itself. In the " Lay of the 
Last Minstrel," Scott gives an account of the way in which 
the Lady of Buccleuch applied this occult surgery to the 
wound of William of Deloraine : 

44 She drew the splinter from the wound, 

And with a charm she stanched the blood. 

She bade the gash be cleansed and bound: 

No longer by his couch she stood ; 
But she has ta'en the broken lance. 

And washed it from the clotted gore, 

And salved the splinter o'er and o'er. 
William of Deloraine, in trance, 
Whene'er she turned it round and round 
Twisted as if she galled his wound. 

Then to her maidens she did say, 
That he should be whole man and sound, 

Within the course of a night and day. 
Full long she toiled, for she did rue 

Mishap to friend so stout and true." 1 

That no direct benefit could have been derived from 
such a mode of treatment must be obvious, but De Morgan 
very plausibly claims that in the then state of surgical and 
medical knowledge, it was really the very best that could 
have been adopted. His argument is as follows : " The 
1 Canto III. Stanza 23. 


sympathetic powder was that which cured by anointing the 
weapon with its salve instead of the wound. I have been 
long convinced that it was efficacious. The directions 
were to keep the wound clean and cool, and to take care of 
diet, rubbing the salve on the knife or sword. If we re- 
member the dreadful notions upon drugs which prevailed, 
both as to quantity and quality, we shall readily see that 
any way of not dressing the wound, would have been use- 
ful. If the physicians had taken the hint, had been careful 
of diet, etc., and had poured the little barrels of medicine 
down the throat of a practicable doll, they would have had 
their magical cures as well as the surgeons. Matters are 
much improved now ; the quantity of medicine given, even 
by orthodox physicians, would have been called infinitesi- 
mal by their professional ancestors. Accordingly, the 
College of Physicians has a right to abandon its motto, 
which is, Ars longa, vita brevis, meaning, Practice is long, 
so life is short." 

As set forth by Digby and others, the use of the Powder 
of Sympathy is free from all taint of witchcraft or magic, 
but, in another form, it was wholly dependent upon incanta- 
tions and other magical performances. This idea of sym- 
pathetic action was even carried so far as to lead to attempts 
to destroy or injure those whom the operator disliked. In 
some cases this was done by moulding an image in wax 
which, when formed under proper occult influences, was 
supposed to have the power of transferring to the victim 
any injuries inflicted on the image. Into such images pins 
and knives were thrust in the hope that the living original 
would suffer the same pains and mutilations that would be 
inflicted if the knives or pins were thrust into him, and 
sometimes the waxen form was held before the fire and 


allowed to melt away slowly in the hope that the prototype 
would also waste away, and ultimately die. Shakespeare 
alludes to this in the play of King John. In Act v., Scene 
4, line 24, Melun says : 

" A quantity of life 

Which bleeds away, even as a form of wax, 
Resolveth from his figure 'gainst the fire ? " 

And Hollinshed tells us that "it was alleged against 
Dame Eleanor Cobham and her confederates that they had 
devised an image of wax, representing the king, which, by 
their sorcerie, by little and little consumed, intending 
thereby, in conclusion, to waste and destroy the king's 

In these cases, however, the operator always depended 
upon certain occult or demoniacal influences, or, in other 
words, upon the art of magic, and therefore examples of 
this kind do not come within the scope of the present 
volume. In the case of the Powder of Sympathy the 
results were supposed to be due entirely to natural causes. 



HIS subject has now found its way not only into 
semi-scientific works but into our general litera- 
ture and magazines. Even our novel-writers 
have used suggestions from this hypothesis as 
part of the machinery of their plots so that it properly 
finds a place amongst the subjects discussed in this 

Various attempts have been made to explain what is 
meant by "the fourth dimension," but it would seem that 
thus far the explanations which have been offered are, to 
most minds, vague and incomprehensible, this latter condi- 
tion arising from the fact that the ordinary mind is utterly 
unable to conceive of any such thing as a dimension which 
cannot be defined in terms of the three with which we are 
already familiar. And I confess at the start that I labor 
under the superlative difficulty of not being able to form 
any conception of a fourth dimension, and for this incapac- 
ity my only consolation is, that in this respect I am not alone. 
I have conversed upon the subject with many able mathe- 
maticians and physicists, and in every case I found that 
they were in the same predicament as myself, and where I 
have met men who professed to think it easy to form a 
conception of a fourth dimension, I have found their ideas, 
not only in regard to the new hypothesis, but to its corre- 



lations with generally accepted physical facts, to be nebu- 
lous and inaccurate. 

It does not follow, however, that because myself and 
some others cannot form such a clear conception of a fourth 
dimension as we can of the third, that, therefore, the theory 
is erroneous and the alleged conditions non-existent. Some 
minds of great power and acuteness have been incapable 
of mastering certain branches of science. Thus Diderot, 
who was associated with d'Alembert, the famous mathe- 
matician, in the production of " L'Encyclopedie," and who 
was not only a man of acknowledged ability, but who, at one 
time, taught mathematics and wrote upon several mathe- 
matical subjects, seems to have been unable to master the 
elements of algebra. The following anecdote regarding 
his deficiency in this respect is given by Thiebault and 
indorsed by Professor De Morgan : At the invitation of 
the Empress, Catherine II, Diderot paid a visit to the 
Russian court. He was a brilliant conversationalist and 
being quite free with his opinions, he gave the younger 
members of the court circle a good deal of lively atheism. 
The Empress herself was very much amused, but some of 
her councillors suggested that it might be desirable to 
check these expositions of strange doctrines. As Cathe- 
rine did not like to put a direct muzzle on her guest's tongue, 
the following plot was contrived. Diderot was informed 
that a learned mathematician was in possession of an al- 
gebraical demonstration of the existence of God and would 
give it to him before all the court if he desired to hear it. 
Diderot gladly consented, and although the name of the 
mathematician is not given, it is well known to have been 
Euler. He advanced toward Diderot, and said in French, 
gravely, and in a tone of perfect conviction : " Monsieur, 


- = x t therefore, God exists; reply!" Diderot, to 

whom algebra was Hebrew, was embarrassed and discon- 
certed, while peals of laughter rose on all sides. He asked 
permission to return to France at once, which was granted. 
Even such a mind as that of Buckle, who was generally 
acknowledged to be a keen-sighted thinker, could not form 
any idea of a geometrical line that is, of a line without 
breadth or thickness, a conception which has been grasped 
clearly and accurately by thousands of school-boys. He 
therefore asserts, positively, that there are no lines without 
breadth, and comes to the following extraordinary conclu- 
sions : 

" Since, however, the breadth of the faintest line is so 
slight as to be incapable of measurement, except by an 
instrument under the microscope, it follows that the as- 
sumption that there can be lines without breadth is so 
nearly true that our senses, when unassisted by art, can 
not detect the error. Formerly, and until the invention of 
the micrometer, in the seventeenth century, it was im- 
possible to detect it at all. Hence, the conclusions of the 
geometrician approximate so closely to truth that we are 
justified in accepting them as true. The flaw is too minute 
to be perceived. But that there is a flaw appears to me 
certain. It appears certain that, whenever something is 
kept back in the premises, something must be wanting 
in the conclusion. In all such cases, the field of inquiry 
has not been entirely covered; and part of the preliminary 
facts being suppressed, it must, I think, be admitted that 
complete truth be unattainable, and that no problem in 
geometry has been exhaustively solved." 1 

The fallacy which underlies Mr. Buckle's contention is 
thus clearly exposed by the author of " The Natural His- 
tory of Hell." 

1 "History of Civilization in England." American edition, Vol. 
II, page 342. 


"If it be conceded that lines have breadth, then all we 
have to do is to assign some definite breadth to each line 
say the one-thousandth of an inch and allow for it. 
But the lines of the geometer have no breadth. All the 
micrometers of which Mr. Buckle speaks depend, either 
directly or indirectly, upon lines for their graduations, and 
the positions of these lines are indicated by rulings or 
scratches. Now, in even the finest of these rulings, as, 
for example, those of Nobert or Fasoldt, where the ruling 
or scratching, together with its accompanying space, 
amounts to no more than the one hundred and fifty thou- 
sandth part of an inch, the scratch has a perceptible breadth. 
But this broad scratch is not the line recognized by the 
microscopist, to say nothing of the geometer. The true 
line is a line which lies in the very center of this scratch 
and it is certain that this central line has absolutely no 
breadth at all." l 

It must be very evident that if Mr. Buckle's contention 
that geometrical lines have breadth were true, then some 
of the fundamental axioms of geometry must be false. It 
could no longer hold true that " the whole is equal to all its 
parts taken together," for if we divide a square or a circle 
into two parts by means of a line which has breadth, the 
two parts cannot be equal to the whole as it formerly was. 
As a matter of fact, Mr. Buckle's lines are saw-cuts, not 
geometrical lines. Geometrical points, lines, and surfaces, 
have no material existence and can have none. An ideal 
conception and a material existence are two very different 

A very interesting book 2 has been written on tbe move- 
ments and feelings of the inhabitants of a world of two di- 
mensions. Nevertheless, if we know anything at all, we 
know that such a world could not have any actual existence 

1 "The Natural History of Hell," by John Phillipson, page 37. 
* " Flatland," by E. A. Abbott. London, 1884. 


and when we attempt to form any mental conception of it 
and its inhabitants, we are compelled to adopt, to a certain 
extent, the idea of the third dimension. 

But at the same time we must remember that since the 
ordinary mechanic and the school-boy who has studied ge- 
ometry, find no difficulty in conceiving of points without 
magnitude, lines without breadth, and surfaces without 
thickness conceptions which seem to have been impos- 
sible to Buckle, a man of acknowledged ability it may be 
possible that minds constituted slightly differently from 
that of myself and some others, might, perhaps, be able to 
form a conception of a fourth dimension. 

Leaving out of consideration the speculations of those 
who have woven this idea into romances and clay-dreams we 
find that the hypothesis of a fourth dimension has been 
presented by two very different classes of thinkers, and 
the discussion has been carried on from two very different 

The first suggestion of this hypothesis seems to have 
come from Kant and Gauss and to have had a purely meta- 
physical origin, for, although attempts have been made to 
trace the idea back to the famous phantoms of Plato, it is 
evident that the ideas then advanced had nothing in com- 
mon with the modern theory of the existence of a fourth 
dimension. The first hint seems to have been a purely 
mathematical one and did not attract any very general at- 
tention. It was, however, seized upon by a certain branch 
of the transcendentalists, closely allied to the spiritualists, 
and was exploited by them as a possible explanation of 
some curious and mysterious phenomena and feats exhibited 
by certain Indian and European devotees. This may have 
been done merely for the purpose of mystifying and con- 


founding their adversaries by bringing forward a striking 
illustration of Hamlet's famous dictum " 

''There are more things in heaven and earth, Horatio, 
Than are dreamt of in your philosophy." 

A very fair statement of this view is thus given by 
Edward Carpenter : 1 

" There is another idea which modern science has been 
familiarizing us with, and which is bringing us towards 
the same conception that, namely, of the fourth dimen- 
sion. The supposition that the actual world has four 
space-dimensions instead of three makes many things 
conceivable which otherwise would be incredible. It makes 
it conceivable that apparently separate objects, e. g., dis- 
tinct people, are really physically united; that things ap- 
parently sundered by enormous distances of space are 
really quite together; that a person or other object might 
pass in and out of a closed room without disturbance of 
walls, doors or windows, etc., and if this fourth dimension 
were to become a factor of our consciousness it is obvious 
that we should have means of knowledge which, to the 
ordinary sense, would appear simply miraculous. There is 
much, apparently, to suggest that the consciousness at- 
tained to by the Indian gfianis in their degree, and by 
hypnotic subjects in theirs, is of this fourth dimensional 

" As a solid is related to its own surface, so, it would 
appear, is the cosmic consciousness related to the ordinary 
consciousness. The phases of the personal consciousness 
are but different facets of the other consciousness; and 
experiences which seem remote from each other in the in- 
dividual are perhaps all equally near in the universal. 
Space itself, as we know it, may be practically annihilated 
in the consciousness of a larger space, of which it is but the 
superficies; and a person living in London may not un- 
likely find that he has a back door opening quite simply 
and unceremoniously out in Bombay." 

On the other hand, the mathematicians, looking at it as 
a purely speculative idea, have endeavored to arrive at 

1 " From Adam's Peak to Elephanta " page 160. 


definite conclusions in regard to what would be the condi- 
tion of things if the universe really exists in a fourth, or 
even in some higher dimension. Professor W. W. R. Ball 
tells us that 

" the conception of a world of more than three dimensions 
is facilitated by the fact that there is no difficulty in imagin- 
ing a world confined to only two dimensions which we 
may take for simplicity to be plane though equally 
well it might be a spherical or other surface. We may 
picture the inhabitants of flatland as moving either on the 
surface of a plane or between two parallel and adjacent 
planes. They could move in any direction along the 
plane, but they could not move perpendicularly to it, and 
would have no consciousness that such a motion was 
possible. We may suppose them to have no thickness, 
in which case they would be mere geometrical abstractions ; 
or we may think of them as having a small but uniform 
thickness, in which case they would be realities." 

"If an inhabitant of flatland was able to move in three 
dimensions, he would be credited with supernatural powers 
by those who were unable so to move ; for he could appear 
or disappear at will ; could (so far as they could tell) create 
matter or destroy it, and would be free from so many con- 
straints to which the other inhabitants were subject that his 
actions would be inexplicable to them." 

" Our conscious life is in three dimensions, and natur- 
ally the idea occurs whether there may not be a fourth 
dimension. No inhabitant of flatland could realize what 
life in three dimensions would mean, though, if he evolved 
an analytical geometry applicable to the world in which 
he lived, he might be able to extend it so as to obtain results 
true of that world in three dimensions which would be to 
him unknown and inconceivable. Similarly we cannot 
realize what life in four dimensions is like, though we can 
use analytical geometry to obtain results true of that world, 
or even of worlds of higher dimensions. Moreover, the 
analogy of our position to the inhabitants of flatland en- 


ables us to form some idea of how inhabitants of space of 
four dimensions would regard us." 

" If a finite solid was passed slowly through flatland, the 
inhabitants would be conscious only of that part of it which 
was in their plane. Thus they would see the shape of the 
object gradually change and ultimately vanish. In the 
same way, if a body of four dimensions was passed through 
our space, we should be conscious of it only as a solid 
body (namely, the section of the body by our space) whose 
form and appearance gradually changed and perhaps ul- 
timately vanished. It has been suggested that the birth, 
growth, life, and death of animals, may be explained thus 
as the passage of finite four-dimensional bodies through 
our three-dimensional space." 

Attempts have been made to construct drawings and 
models showing a four-dimensional body. The success of 
such attempts has not been very encouraging. 

Investigators of this class look upon the actuality of a 
fourth dimension as an unsolved question, but they hold 
that, provided we could see our way clear to adopt it, it 
would open up wondrous possibilities in the way of explain- 
ing abstruse and hitherto inexplicable physical conditions 
and phenomena. 

There is obviously no limit to such speculations, provided 
we assume the existence of such conditions as are needed 
for our purpose. Too often, however, those who indulge 
in such day-dreams begin by assuming the impossible, and 
end by imagining the absurd. 

We have so little positive knowledge in regard to the 
ultimate constitution of matter and even in regard to the 
actual character of the objects around us, which are revealed 
to us through our senses, that the field in which our imagin- 
ation may revel is boundless. Perhaps some day the 


humanity of the present will merge itself into a new race, 
endowed with new senses, whose revelations are to us, for 
the present, at least, utterly inconceivable. 

The possibility of such a development may be rendered 
more clear if we imagine the existence of a race devoid of 
the sense of hearing, and without the organs necessary to 
that sense. They certainly could form no idea of sound, 
far less could they enjoy music or oratory, such as afford 
us so much delight. And, if one or more of our race should 
visit these people, how very strange to them would appear 
those curious appendages, called ears, which project from 
the sides of our heads, and how inexplicable to them would 
be the movements and expressions of intelligence which we 
show when we talk or sing ? It is certain that no devel- 
opment of the physical or mathematical sciences could give 
them any idea whatever of the sensations which sound, in 
its various modifications, imparts to us, and neither can any 
progress in that direction enable us to acquire any idea of 
the revelations which a new sense might open up to us. 
Nevertheless, it seems to me that the development of new 
senses and new sense organs is not only more likely to be 
possible, but that it is actually more probable, than any 
revelation in regard to a fourth dimension. 


HE following is a curious illustration of the errors 
to which careless observers may be subject : 

Draw a square, like Fig. 19, and divide the sides 
into 8 parts each. Join the points of division in 
opposite sides so as to divide the whole square into 64 
small squares. Then draw the lines shown in black and cut 
up the drawing into four pieces. The lines indicating the 
cuts have been made quite heavy so as to show up clearly, 

Fig. 19. 

Fig. 20. 

but on the actual card they may be made quite light. Now, 
put the four pieces together, so as to form the rectangle 
shown in Fig. 20. Unless the scale, to which the drawing 
is made is quite large and the work very accurate, it will 
seem that the rectangle contains 5 squares one way and 
13 the other which, when multiplied together, give 65 for 
the number of small squares, being an apparent gain of 
one square by the simple process of cutting. 


This paradox is very apt to puzzle those who are not 
familiar with accurate drawings. Of course, every person of 
common sense knows that the card or drawing is not made 
any larger by cutting it, but where does the 65th small 
square come from ? 

On careful examination it will be seen that the line AB, 
Fig. 20, is not quite straight and the three parts into which 
it is divided are thus enabled to gain enough to make one 
of the small squares. On a small scale this deviation from 
the straight line is not very obvious, but make a larger draw- 
ing, and make it carefully, and it will readily be seen how 
the trick is done. 


THINK it was the elder Stephenson, the famous 
engineer, who told a man who claimed the 
honor of having invented a perpetual motion, 
that when he could lift himself over a fence by 
taking hold of his waist-band, he might hope to accomplish 
his object. And the query which serves as a title for this 
article has long been propounded as one of the physical 
impossibilities. And yet, perhaps, it might be possible to 
invent a waist-band or a boot-strap by which this apparently 
impossible feat might be accomplished ! 

Travelers in Mexico frequently bring home beans which 
jump about when laid on a table. They are well-known as 
"jumping beans" and have often been a puzzle to those 
who were not familiar with the facts in the case. Each 
bean contains the larva of a species of beetle and this af- 
fords a clue to the secret. But the question at once comes 
up : " How is the insect able to move, not only itself, but its 
house as well, without some purchase or direct contact with 
the table?" 

The explanation is simple. The hollow bean is elastic 
and the insect has strength enough to bend it slightly ; 
when the insect suddenly relaxes its effort and allows the 
bean to spring back to its former shape, the reaction on 
the table moves the bean. A man placed in a perfectly 
rigid box could never move himself by pressing on the 
sides, but if the box were elastic and could be bent by the 
strength of the man inside, it might be made to move. 



A somewhat analogous result, but depending on different 
principles, is attained in certain curious boat races which 
are held at some English regattas and which is explained 
by Prof. W. W. Rouse Ball, in his " Mathematical Recrea- 
tions and Problems." He says that it 

" affords a somewhat curious illustration of the fact that 
commonly a boat is built so as to make the resistance to 
motion straight forward less than that to motion in the 
opposite direction. 

" The only thing supplied to the crew is a coil of rope, 
and they have (without leaving the boat) to propel it from 
one point to another as rapidly as possible. The motion 
is given by tying one end of the rope to the afterthwart, 
and giving the other end a series of violent jerks in a 
direction parallel to the keel. 

" The effect of each jerk is to compress the boat. Left 
to itself the boat tends to resume its original shape, but 
the resistance to the motion through the water of the 
stern is much greater than that of the bow, hence, on the 
whole, the motion is forwards. I am told that in still water 
a pace of two or three miles an hour can be thus attained." 


|NE of the most interesting books in natural his- 
tory is a work on " Insect Architecture," by 
Rennie. But if the architecture of insect 
homes is wonderful, the engineering displayed 
by these creatures is equally marvellous. Long before man 
had thought of the saw, the saw-fly had used the same tool, 
made after the same fashion, and used in the same way for 
the purpose of making slits in the branches of trees so that 
she might have a secure place in which to deposit her 
eggs. The carpenter bee, with only the tools which nature 
has given her, cuts a round hole, the full diameter of her 
body, through thick boards, and so makes a tunnel by which 
she can have a safe retreat, in which to rear her young. 
The tumble-bug, without derrick or machinery, rolls over 
large masses of dirt many times her own weight, and the 
sexton beetle will, in a few hours, bury beneath the ground 
the carcass of a comparatively large animal. All these feats 
require a degree of instinct which in a reasoning creature 
would be called engineering skill, but none of them are as 
wonderful as the feats performed by the spider. This ex- 
traordinary little animal has the faculty of propelling her 
threads directly against the wind, and by means of her 
slender cords she can haul up and suspend bodies which 
are many times her own weight. 

Some years ago a paragraph went the rounds of the 
papers in which it was said that a spider had suspended an 
unfortunate mouse, raising it up from the ground, and 



leaving it to perish miserably between heaven and earth. 
Would-be philosophers made great fun of this statement, 
and ridiculed it unmercifully. I know not how true it was, 
but I know that it migJit have been true. 

Some years ago, in the village of Havana, in the State of 
New York, a spider entangled a milk-snake in her threads, 
and actually raised it some distance from the ground, 
and this, too, in spite of the struggles of the reptile, which 
was alive. 

By what process of engineering did the comparatively 
small and feeble insect succeed in overcoming and lifting up 
by mechanical means, the mouse or the snake ? The solution 
is easy enough if we only give the question a little thought. 

The spider is furnished with one of the most efficient 
mechanical implements known to engineers, viz., a strong 
elastic thread. That the thread is strong is well known. 
Indeed, there are few substances that will support a greater 
strain than the silk of the silkworm, or the spider ; careful 
experiment having shown that for equal sizes the strength 
of these fibers exceeds that of common iron. But notwith- 
standing its strength, the spider's thread alone would be 
useless as a mechanical power if it were not for its elasticity. 
The spider has no blocks or pulleys, and, therefore, it cannot 
cause the thread to divide up and run in different directions, 
but the elasticity of the thread more than makes up for 
this, and renders possible the lifting of an animal much 
heavier than a mouse or a snake. This may require a little 

Let us suppose that a child can lift a six-pound weight 
one foot high and do this twenty times a minute. Furnish 
him with 350 rubber bands, each capable of pulling six 
pounds through one foot when stretched. Let these bands 


be attached to a wooden platform on which stand a pair 
of horses weighing 2,100 Ibs., or rather more than a ton. 
If now the child will go to work and stretch these rubber 
bands, singly, hooking each one up, as it is stretched, in 
less than twenty minutes he will have raised the pair of 
horses one foot ! 

We thus see that the elasticity of the rubber bands 
enables the child to divide the weight of the horses into 
350 pieces of six pounds each, and at the rate of a little less 
than one every three seconds, he lifts all these separate pieces 
one foot, so that the child easily lifts this enormous weight. 

Each spider's thread acts like one of the elastic rubber 
bands. Let us suppose that the mouse or the snake weighed 
half an ounce and that each thread is capable of supporting 
a grain and a half. The spider would have to connect the 
mouse with the point from which it was to be suspended 
with 150 threads, and if the little quadruped was once 
swung off his feet, he would be powerless. By pulling 
successively on each thread and shortening it a little, the 
mouse or snake might be raised to any height within the 
capacity of the building or structure in which the work was 
done. So that to those who have ridiculed the story we 
may justly say: "There are more things in heaven and 
earth than are dreamed of in your philosophy." 

What object the spider could have had in this work I 
am unable to see. It may have been a dread of the harm 
which the mouse or snake might work, or it may have been 
the hope that the decaying carcass would attract flies which 
would furnish food for the engineer. I can vouch for the 
truth of the snake story, however, and the object of this 
article is to explain and render credible a very extraordinary 
feat of insect engineering. 





N the twentieth chapter of II Kings, at the 
eleventh verse we read, that "Isaiah the prophet 
cried unto the Lord, and he brought the shadow 
ten degrees backward, by which it had gone 
down in the dial of Ahaz." 

It is a curious fact, first pointed out by Nonez, the 
famous cosmographer and mathematician of the sixteenth 
century, but not generally known, that by tilting a sun-dial 
through the proper angle, the shadow at certain periods of 
the year can be made, for a short time, to move backwards 
on the dial. This was used by the French encyclopaedists 
as a rationalistic explanation of the miracle which is related 
at the opening of this article. 

The reader who is curious in such matters will find direc- 
tions for constructing "a dial, for any latitude, on which 
the shadow shall retrograde or move backwards," in 
Ozanam's " Recreations in Science and Natural Philosophy," 
Riddle's edition, page 529. Professor Ball in his "Mathe- 
matical Recreations," page 214, gives a very clear explana- 
tion of the phenomenon. The subject is somewhat too 
technical for these pages. 


EVERAL years ago a correspondent of " Truth " 
(London) gave the following simple directions for 
finding the points of the compass by means of 
the ordinary pocket watch : " Point the hour hand 
to the sun, and south is exactly half way between the hour 
hand and twelve on the watch, counting forward up to 
noon, but backward after the sun has passed the meridian." 
Professor Ball, in his " Mathematical Recreations and 
Problems," gives more complete directions and explanations. 
He says : 

" The position of the sun relative to the points of the 
compass determines the solar time. Conversely, if we 
take the time given by a watch as being the solar time 
(and it will differ from it only by a few minutes at the 
most), and we observe the position of the sun, we can find 
the points of the compass. To do this it is sufficient to 
point the hour-hand to the sun and then the direction which 
bisects the angle between the hour and the figure XII will 
point due south. For instance, if it is four o'clock in the 
afternoon, it is sufficient to point the hour-hand (which 
is then at the figure IIII) to the sun, and the figure II on 
the watch will indicate the direction of south. Again, if 
it is eight o'clock in the morning, we must point the hour- 
hand (which is then at the figure VIII) to the sun, and the 
figure X on the watch gives the south point of the compass. 

" Between the hours of six in the morning and six in 
the evening the angle between the hour and XII, which 
must be bisected is less than 180 degrees, but at other times 
the angle to be bisected is greater than 180 degrees; or per- 
haps it is simpler to say that at other times the rule gives 
the north point and not the south point. 

"The reason is as follows: At noon the sun is due 



south, and it makes one complete circuit round the points 
of the compass in 24 hours. The hour-hand of a watch 
also makes one complete circuit in 12 hours. Hence, if 
the watch is held with its face in the plane of the ecliptic, 
and the figure XII on the dial is pointed to the south, both 
the hour-hand and the sun will be in that direction at noon. 
Both move round in the same direction, but the angular 
velocity of the hour-hand is twice as great as that of the 
sun. Hence the rule. The greatest error due to the neglect 
of the equation of time is less than 2 degrees. Of course, 
in practice, most people would hold the face of the watch 
horizontal, and in our latitude (that of London) no serious 
error would thus be introduced. 

" In the southern hemisphere, or in any tropical country 
where at noon the sun is due north, the rule will give the 
north point instead of the south." 


INUTE works of art have always excited the 
curiosity and commanded the admiration of the 
average man. Consequently Cicero thought it 
worth while to record that the entire Illiad of 
Homer had been written upon parchment in characters so 
fine that the copy could be enclosed in a nutshell. This 
has always been regarded as a marvelous feat. 

There is in the French Cabinet of Medals a seal, said to 
have belonged to Michael Angelo, the fabrication of which 
must date from a very remote epoch, and upon which fifteen 
figures have been engraved in a circular space of fourteen 
millimeters (.55 inch) in diameter. These figures cannot 
be distinguished by the naked eye. 

The Ten Commandments have been engraved in charac- 
ters so fine that they could be stamped upon one side of a 
nickle five-cent piece, and on several occasions the Lord's 
Prayer has been engraved on one side of a gold dollar, the 
diameter of which is six-tenths of an inch. I have also 
seen it written with a pen within a circle which measured 
four-tenths of an inch in diameter. 

In the Harleian manuscript, 530, there is an account of a 
"rare piece of work, brought to pass by Peter Bales, an 
Englishman, and a clerk of the chancery." Disraeli tells 
us that it was " The whole Bible in an English walnut, no 
bigger than a hen's egg. The nut holdeth the book : there 
are as many leaves in his little book as in the great Bible, 



and he hath written as much in one of his little leaves as 
a great leaf of the Bible." 

By most people, such achievements are considered mar- 
vels of skill, and the newspaper accounts of them which are 
published always attract special attention. And it must 
be acknowledged that such work requires good eyes, steady 
nerves, and very delicate control of the muscles. But with 
ordinary writing materials there are certain mechanical 
limitations which must prevent even the most skilful from 
going very far in this direction. These limitations are im- 
posed by the fiber or grain of the paper and the construc- 
tion of the ordinary pen, neither of which can be carried 
beyond a certain very moderate degree of fineness. Of 
course, the paper that is chosen will be selected on account 
of its hard, even-grained surface, and the pen will be chosen 
on account of the quality of its material and its shape, and 
the point is always carefully dressed on a whetstone so as 
to have both halves of the nib equal in strength and length, 
and the ends smooth and delicate. When due preparation 
has been made, and when the eyes and nerves of the writer 
are in good condition, the smallness of the distinctly read- 
able letters that may be produced is wonderful. And in 
this connection it is an interesting fact that in many me- 
chanical operations, writing included, the hand is far more 
delicate than the eye. That which the unaided eye can 
see to write, the unaided eye can see to read, but the hand, 
without the assistance or guidance of the eye, can produce 
writing so minute that the best eyes cannot see to read it, 
and yet, when viewed under a microscope, it is found to 
compare favorably with the best writing of ordinary size. 
And those who are conversant with the more delicate 
operations of practical mechanics, know that this is no ex- 


ceptional case. The only aid given by the eye in the case 
of such minute writing is the arrangement of the lines, 
otherwise the writing could be done as well with the eyes 
shut as open. 

Since the mechanical limitations which we have noted 
prevent us from going very far with the instruments and 
materials mentioned, the next step is to adopt a finer sur- 
face and a sharper point. These conditions may be found 
in the fine glazed cards and the metal pencils or styles used 
by card writers. In these cards the surface is nearly homo- 
geneous, that is to say, free from fibers, and the point of 
the metal pencil may be made as sharp as a needle, but to 
utilize these conditions to the fullest extent, it is necessary 
to aid the eye, and a magnifier is, therefore, brought into 
use. Under a powerful glass the hand may be so guided 
by the eye that the writing produced cannot be read by the 
unaided vision. 

The specimens of fine writing thus far described have 
been produced directly by the hand under the guidance 
either of a magnifier or the simple sense of motion. Just 
how far it would be possible to go by these means has 
never been determined, so far as I know, but those who 
have examined the specimens of selected diatoms and in- 
sect scales in which objects that are utterly invisible to the 
naked eye are arranged with great accuracy so as to form 
the most beautiful figures, can readily believe that a com- 
bination of microscopical dexterity and skill in penmanship 
might easily go far beyond anything that has yet been ac- 
complished in this direction, either in ancient or modern 

But by means of a very simple mechanical arrangement, 
the motion of the hand in every direction may be accurately 


reduced or enlarged to almost any extent, and it thus 
becomes possible to form letters which are inconceivably 
small. The instrument by which this is accomplished is 
known as a pantagraph, and it has, within a few years, 
become quite popular as a means of reducing or enlarging 
pictures of various kinds, including crayon reproductions 
of photographs. Its construction and use are, therefore, 
very generally understood. It was by means of a very 
finely-made instrument embodying the principles of the 
pantagraph that the extraordinarily fine work which we 
are about to describe was accomplished. 

It is obvious, however, that in order to produce very fine 
writing we must use a very fine pen or point and the finer 
the point the sooner does it wear out, so that in a very 
short time the lines which go to form the letters become 
thick and blurred and the work is rendered illegible. As 
a consequence of this, when the finest specimens of writing 
are required, it is necessary to abandon the use of ordinary 
points and surfaces and to resort to the use of the diamond 
for a pen, and glass for a surface upon which to write. One 
of the earliest attempts in this direction was that of M. 
Froment, of Paris, who engraved on glass, within a circle, 
the one-thirtieth of an inch in diameter, the Coat of Arms 
of England lion, unicorn, and crown with the following 
inscription, partly in Roman letters, partly in script : " Honi 
soit qid mat y pensc, Her Most Gracious Majesty, Queen 
Victoria, and His Royal Highness, Prince Albert, Dieu et 
mon droit. Written on occasion of the Great Exhibition, 
by Froment, a Paris, 1851." 

The late Dr. Barnard, President of Columbia College, 
had in his possession a copy of the device borne by the seal 
of Columbia College, New York, executed for him by M. 


Dumoulin-Froment, within a circle less than three one- 
hundredths of an inch in diameter, " in which are embraced 
four human figures and various other objects, together with 
inscriptions in Latin, Greek, and Hebrew, all clearly legible. 
In this device the rising sun is represented in the horizon, 
the diameter of the disk being about three one-thousandths 
of an inch. This disk has been cross-hatched by the 
draughtsman in the original design from which the copy 
was made ; and the copy shows the marks of the cross- 
hatching with perfect distinctness. When this beautiful 
and delicate drawing is brought clearly out by a suitably 
adjusted illumination, the lines appear as if traced by a 
smooth point in a surface of opaque ice." 

Lardner, in his book on the " Microscope," published in 
1856, gives a wood cut which shows the first piece of en- 
graving magnified 1 20 diameters, but he said that he was 
not at liberty to describe the method by which it was 
done. As happens in almost all such cases, however, the 
very secrecy with which the process was surrounded natu- 
rally stimulated others to rival or surpass it, and Mr. N. 
Peters, a London banker, turned his attention to the subject 
and soon invented a machine which produced results far 
exceeding anything that M. Froment had accomplished. 
On April 25, 1855, Mr. Farrants read before the Microsco- 
pical Society'of London a full account of the Peters machine, 
with which the inventor had written the Lord's Prayer (in 
the ordinary writing character, without abbreviation or 
contraction of any kind), in a space not exceeding the one 
hundred and fifty-thousandth of a square inch. Seven 
years later, Mr. Farrants, as President of the Microscopical 
Society, described further improvements in the machine of 
Mr. Peters, and made the following statement : " The 


Lord's Prayer has been written and may be read in the 
one-three hundred and fifty-six thousandth of an English 
square inch. The measurements of one of these specimens 
was verified by Dr. Bowerbank, with a difference of not 
more than one five-millionth of an inch, and that difference, 
small as it is, arose from his not including the prolongation 
of the letter/ in the sentence 'deliver us from evil ' ; so 
he made the area occupied by the writing less than that 
stated above." 

Some idea of the minuteness of the characters in these 
specimens may be obtained from the statement that the 
whole Bible and Testament, in writing of the same size, 
might be placed twenty-two times on the surface of a square 
inch. The grounds for this startling assertion are as 
follows : " The Bible and Testament together, in the English 
language, are said to contain 3,566,480 letters. The num- 
ber of letters in the Lord's Prayer, as written, ending in 
the sentence, 'deliver us from evil,' is 223, whence, as 
3,566,480 divided by 223, is equal to 15,922, it appears 
that the Bible and Testament together contain the same 
number of letters as the Lord's Prayer written 16,000 
times; if then the prayer were written in 1-16,000 of an 
inch, the Bible and Testament in writing of the same size 
would be contained by one square inch ; but as i-356,oooth 
of an inch is one twenty-secondth part of 1-15,922 of an 
inch, it follows that the Bible and Testament, in writing of 
that size, would occupy less space than one twenty-secondth 
of a square inch." 

It only now remains to be seen that, minute as are the 
letters written by this machine, they are characterized by a 
clearness and precision of form which proves that the mov- 
ing parts of the machine, while possessing the utmost 


delicacy of freedom, are absolutely destitute of shake, a 
union of requisites very difficult of fulfilment, but quite 
indispensable to the satisfactory performance of the ap- 

I have no information in regard to the present where- 
abouts of any of the specimens turned out by Mr. Peters, 
and inquiry in London, among persons likely to know, has 
not supplied any information on the subject. 

There was, however, another micrographer, Mr. William 
Webb, of London, who succeeded in producing some mar- 
vellous results. Epigrams and also the Lord's Prayer 
written in the one-thousandth part of a square inch have 
been freely distributed. Mr. Webb also produced a few 
copies of the second chapter of the Gospel, according to St. 
John, written on the scale of the whole Bible, to a little 
more than three-quarters of a square inch, and of the Lord's 
Prayer written on the scale of the whole Bible eight times 
on a square inch. Mr. Webb died about fifteen years ago, 
and I believe he has had no successor in the art. Speci- 
mens of his work are quite scarce, most of them having 
found their way into the cabinets of public Museums and 
Societies, who are unwilling to part with them. The late 
Dr. Woodward, Director of the Army Medical Museum, 
Washington, D.C., procured two of them on special order 
for the Museum. Mr. Webb had brought out these fine 
writings as tests for certain qualities of the microscope, and 
it was to "serve as tests for high-power objectives" that 
Dr. Woodward procured the specimens now in the micro- 
scopical department of the Museum. I am so fortunate as 
to have in my possession two specimen's of Mr. Webb's 
work. One is an ordinary microscopical glass slide, three 
inches by one, and in the center is a square speck which 


measures 1-4 5th of an inch on the side. Upon this square 
is written the whole of the second chapter of the Gospel 
according to St. John the chapter which contains the 
account of the marriage in Cana of Galilee. 

In order to estimate the space which the whole Bible 
would occupy if written on the same scale as this chapter, 
I have made the following calculation which, I think, will be 
more easily followed and checked by my readers, than that 
of Mr. Farrants. 

The text of the old version of the Bible, as published in 
minion by the American Bible Society, contains 1272 
pages, exclusive of title pages and blanks. Each .page 
contains two columns of 58 lines each, making 116 lines 
to the page. This includes the headings of the chapters 
and the synopses of their contents, which are, therefore, 
thrown in to make good measure. We have, therefore, 
1272 pages of 116 lines each, making a total of 147,552 

The second chapter of St. John has 25 verses contain- 
ing 95 lines, and is written on the 1-202 5th of an inch, or, 
in other words, it would go 2025 times on a square inch. 
A square inch would, therefore, contain 95 X 2025 or 
192,375 lines. This number (192,375), divided by the 
number of lines in the Bible (147,552), gives 1.307, which 
is the number of times the Bible might be written on a 
square inch in letters of the same size. In other words, 
the whole Bible might be written on .77 inch, or very little 
more than three-quarters of a square inch. 

Perhaps the following gives a more impressive illustration : 
The United States silver quarter of a dollar is .95 inch in 
diameter, so that the surface of each side is .707 of a square 
inch. The whole Bible would, therefore, very nearly go on 


one side of a quarter of a dollar. If the blank spaces at 
the heads of the chapters and the synopses of contents 
were left out, it would easily go on one side. 

The second specimen, which I have of Mr. Webb's writ- 
ing, is a copy of the Lord's Prayer written on a scale of 
eight Bibles to the square inch. According to a statement 
kindly sent me by the superintendent of the United States 
Mint at Philadelphia, the diameter of the last issued gold 
dollar, and also of the silver half-dime, is six-tenths of an 
inch. This gives .2827+ of a square inch as the area of 
the surface of one side, and, therefore, the whole Bible 
might be written more than two and a quarter times on one 
side of either the gold dollar or the silver half dime. 

Such numerical and space relations are far beyond the 
power of any ordinary mind to grasp. With the aid of a 
microscope we can see the object and compare with other 
magnifications the rate at which it is enlarged, and a per- 
son of even the most ordinary education can follow the 
calculation and understand why the statements are true, 
but the final result, like the duration of eternity or the 
immensity of space, conveys no definite idea to our minds. 

But at the same time we must carefully distinguish 
between our want of power to grasp these ideas and our 
inability to form a conception of some inconceivable sub- 
ject, such as a fourth dimension or the mode of action of a 
new sense. 

Wonderful as these achievements are, there is another 
branch of the microscopic art which, from the practical 
applications that have been made of it, is even more inter- 
esting. This is the art of microphotography. 

About the middle of the last century Mr. J. B. Dancer, 
of Manchester, England, produced certain minute photo- 


graphs of well-known pictures and statues which com- 
manded the universal attention of the microscopists of that 
day, and for a time formed the center of attraction at all 
microscopical exhibitions. They have now, however, be- 
come so common that they receive no special notice. Mr. 
Dancer and other artists also produced copies -of the Lord's 
Prayer, the Creed, the Declaration of Independence, etc., 
on such a scale that the Lord's Prayer might be covered 
with the head of a common pin, and yet, when viewed 
under a very moderate magnifying power, every letter was 
clear and distinct. I have now before me a slip of glass, 
three inches long and one inch wide, in the center of 
which is an oval photograph which occupies less than the 
i-2OOth of a square inch. This photograph contains the 
Declaration of Independence with the signatures of all the 
signers, surrounded by portraits of the Presidents and 
the seals of the original thirteen States. Under a moder- 
ate power every line is clear and distinct. In the same 
way copies of such famous pictures as Landseer's " Stag 
at Bay," although almost invisible to the naked eye, come 
out beautifully clear and distinct under the microscope, so 
that it has been suggested that one might have an exten- 
sive picture gallery in a small box, or pack away copies of 
all the books in the Congressional Library in a small hand- 
bag. With such means at our command, it would be a 
simple matter to condense a bulky dispatch into a few 
little films, which might be carried in a quill or concealed 
in ways which would have been impossible with the origi- 
nal. If Major Andre had been able to avail himself of 
this mode of reducing the bulk of the original papers, he 
might have carried, without danger of discovery, those re- 
ports which caused his capture and led to his death. And 


hereafter the ordinary methods of searching suspected 
spies will have to be exchanged for one that is more 

The most interesting application of microphotography, 
of which we have any record, occurred during the Franco- 
Prussian war in 1870-71. 

On September 21, 1870, the Germans so completely 
surrounded the French capitol, that all communication by 

Fig. 21. 

roads, railways, and telegraphs, was cut off and the only 
way of escape from the city was through the air. On 
April 23, the first balloon left Paris, and in a short time 
after that, a regular balloon post was established, letters 
and packages being sent out at intervals of three to seven 
days. In order to get news back to the city, carrier 
pigeons were employed, and at first the letters were simply 
written on very thin paper and enclosed in quills which 
were fastened to the middle tail-feather of the bird, as 
shown in the engraving, Fig. 21. It is, of course, . need- 


.less to say, that the ordinary pictures of doves with letters 
tied round their necks or love-notes attached to their 
wings, are all mere romance. A bird loaded in that way 
would soon fall a prey to its enemies. As it was, some of 
the pigeons were shot by German gunners or captured by 
hawks trained by the Germans for the purpose, but the 
great majority got safely through. 

Written communications, however, were of necessity, 
bulky and heavy, and therefore M. Dagron, a Parisian 
photographer, suggested that the news be printed in large 
sheets of which microphotographs could be made and trans- 
ferred to collodion positives which might then be stripped 
from the glass and would be very light. This was done; 
the collodion pellicles measuring about ten centimeters 
(four inches) square and containing about three thousand 
average messages. Eighteen of these pellicles weighed 
less than one gramme (fifteen grains) and were easily 
carried by a single pigeon. The pigeons having been bred 
in Paris and sent out by balloons, always returned to their 
dove-cotes in that city. 

M. Dagron left Paris by balloon on November 12, and 
after a most adventurous voyage, being nearly captured by 
a German patrol, he reached Tours and there established 
his headquarters, and organized a regular system of com- 
munication with the capitol. The results were most satis- 
factory, upwards of two and a half millions of messages 
having been sent into the city. Even postal orders, and 
drafts were transmitted in this way and duly honored. 

And thus through the pigeon-post, aided by micropho- 
tography, Paris was enabled to keep in touch with the 
outer world, and the anxiety of thousands of families was 


It is not likely, however, that the pigeon-post will ever 
again come into use for this purpose ; our interest in it 
is now merely historical, for in the next great siege, if we 
ever have one, the wireless telegraph will no doubt take 
its place and messages, which no hawks can capture and no 
guns can destroy, will be sent directly over the heads of 
the besiegers. 

But let us hope and pray, that the savage and unneces- 
sary war which is now being waged in the east will be the 
last, and that in the near future, two or more of the great 
nations of the globe will so police the world, that peace on 
earth and good will toward men will everywhere prevail. 


UR senses have been called the "Five Gateways 
of Knowledge " because all that we know of the 
world in which we live reaches the mind, either 
directly or indirectly, through these avenues. 
From the " ivory palace," in which she dwells apart, and 
which we call the skull, the mind sends forth her scouts 
sight, hearing, feeling, taste, and smell bidding them 
bring in reports of all that is going on around her, and if 
the information which they furnish should be untrue or 
distorted, the most dire results might follow. She, there- 
fore, frequently compares the tale that is told by one with 
the reports from the others, and in this way it is found that 
under some conditions these reporters are anything but 
reliable ; the stories which they tell are often distorted and 
untrue, and in some cases their tales have no foundation 
whatever in fact, but are the "unsubstantial fabric of a 

It is, therefore, of the greatest importance to us, that we 
should find out the points on which these information 
bearers are most likely to be deceived so that we may 
guard against the errors into which they would otherwise 
certainly lead us. 

All the senses are liable to be imposed upon under 
certain conditions. The senses of taste and of smell are 
frequently the subject of phantom smells and tastes, which 
are as vivid as the sensations produced by physical causes 
acting in the regular way. Even those comparatively new 



senses 1 which have been differentiated from the sense of 
touch and which, with the original five, make up the mystic 
number seven, are .very untrustworthy guides under certain 
circumstances. Thus we all know how the sense of heat 
may be deceived by the old experiment of placing one hand 
in a bowl of cold water and the other in a bowl of hot 
water, and then, after a few minutes, placing both hands 
together in a bowl of tepid water ; the hand, which has 
been in the cold water will feel warm, while that which has 
just been taken from the hot water, will feel quite cold. 

We have all experienced the deceptions to which the 
sense of hearing exposes us. Who has not heard sounds 
which had no existence except in our own sensations ? 
And every one is familiar with the illusions to which we 
are liable when under the influence of a skilful ventrilo- 

Even the sense of touch, which most of us regard as 
infallible, is liable to gross deception. When we have 
"felt" anything we are always confident as to its shape, 
number, hardness, etc., but the following very simple ex- 
periment shows that this confidence may be misplaced : 

Take a large pea or a small marble or bullet and place it 

1 The old and generally recognized list of the senses is as follows : Sight, 
Hearing, Smell, Taste, and Touch. This is the list enumerated by John 
Bunyan in his famous work, " The Holie Warre." It has, however, been 
pointed out that the sense which enables us to recognize heat is not quite 
the same as that of touch and modern physiologists have therefore set 
apart, as a distinct sense, the power by which we recognize heat. 

The same had been previously done in the case of the sense of Muscular 
Resistance but, as the author of " The Natural History of Hell " says, 
"when we differentiate the ' Sense of Heat,' and the 'Sense of Resistance* 
from the Sense of Touch, we may set up new signposts, but we do not 
open up any new ' gateways ' , things still remain as they were of old, and 
every messenger from the material world around us must enter the ivory 
palace of the skull through one of the old and well-known ways." 


on the table or in the palm of the left hand. Then cross 
the fingers of the right hand as shown in the engraving, 
Fig. 22, the second finger crossing the first, and place them 
on the ball, so that the latter may lie between the fingers, 

Fig. 22. 

as figured in the cut. If the pea or ball be now rolled 
about, the sensation is apparently that given by two peas 
under the fingers, and this illusion is so strong that it can- 
not be dispelled by calling in any of the other senses (the 
sense of sight for example) as is usually the case under 
similar circumstances. We may try and try, but it will 


only be after considerable experience that we shall learn to 
disregard the apparent impression that there are two balls. 

The cause of this illusion is readily found. In the ordi- 
nary position of the fingers the same ball cannot touch at 
the same time the exterior sides of two adjoining fingers. 
When the two fingers are crossed, the conditions are ex- 
ceptionally changed, but the instinctive interpretation 
remains the same, unless a frequent repetition of the exper- 
iment has overcome the effect of our first education on this 
point. The experiment, in fact has to be repeated a great 
number of times to make the illusion become less and less 

But of all the senses, that of sight is the most liable to 
error and illusion, as the following simple illustrations will 

In Fig. 23 a black spot has been placed on a white 

Fig. 23. Fig. 24. 

ground, and in Fig. 24 a white spot is placed on a black 
ground ; which is the larger, the black spot or the white 
one ? To every eye the white spot will appear to be the 
largest, but as a matter of fact they are both the same size. 
This curious effect is attributed by Helmholtz to what is 
called irradiation. The eye may also be greatly deceived 
even in regard to the length of lines placed side by side. 



Thus, in Fig. 25 a thin vertical line stands upon a thick hor- 
izontal one ; although the two lines are of precisely the 
same length, the vertical one 
seems to be considerably longer 
than the other. I 

In Figs. 26 and 27 a series 
of vertical and horizontal lines 
are shown, and in both forms the 
space that is covered seems to 
be longer one way than the other. 
As a matter of fact the space in 
each case is a perfect square, 
and the apparent difference in 
width and height depends upon whether the lines are ver- 
tical or horizontal. 

Advantage is taken of this curious illusion in dec- 
orating rooms and in selecting dresses. Stout ladies of 
taste avoid dress goods having horizontal stripes, and 

Fig- 25. 

Fig. 26. 

Fig. 27. 

ladies of the opposite conformation avoid those in which the 
stripes are vertical. 

But the greatest discrepancy is seen in Figs. 28 and 29, 
the middle line in Fig. 29 appearing to be much longer 
than in Fig. 28. Careful measurement will show that they 
are both of precisely the same length, the apparent differ- 



ence being due to the arrangement of the divergent lines 
at the ends. 

Converging lines have a curious effect upon apparent 
size. Thus in Fig. 30 we have a wall and three posts, and 




Fig. 28. Fig. 29. 

if asked which of the posts was the highest, most persons 
would name C, but measurement will show that A is the 
highest and that C is the shortest. 

A still more striking effect is produced in two parallel 
lines by crossing them with a series of oblique lines as seen 

Fig. 31. 

in Figs. 3 1 and 32. In Fig. 3 1 the horizontal lines seem to 
be much closer at the right-hand ends than at the left, but 



accurate measurement will show that they are strictly 

By changing the direction of the oblique lines, as shown 
in Fig. 32, the horizontal lines appear to be crooked although 
they are perfectly straight. 

Fig. 3*. 

All these curious illusions are, however, far surpassed by 
an experiment which we will now proceed to describe. 


HE following curious experiment always excites 
surprise, and as I have met with very few persons 
who have ever heard of it, I republish it from 
"The Young Scientist," for November, 1880. 
It throws a good deal of light upon the facts connected 
with vision. 

Procure a paste-board tube about seven or eight inches 

Fig. 33- 

long and an inch or so in diameter, or roll up a strip of any 
kind of stiff paper so as to form a tube. Holding this tube 



in the left hand, look through it with the left eye, the right 
eye also being kept open. Then bring the right hand into 
the position shown in the engraving, Fig. 33, the edge op- 
posite the thumb being about in line with the right-hand 
side of the tube. Or the right hand may rest against the 
right-hand side of the tube, near the end farthest from the 
eye. This cuts off entirely the view of the object by the 
right eye, yet strange to say the object will still remain 
apparently visible to both eyes through a hole in the hand, 
as shown by the dotted lines in the engraving ! In other 
words, it will appear to us as if there was actually a hole 
through the hand, the object being seen through that hole. 
The result is startlingly realistic, and forms one of the 
simplest and most interesting experiments known. 

This singular optical illusion is evidently due to the sym- 
pathy which exists between the two eyes, from our habit of 
blending the images formed in both eyes so as to give a 
single image. 


VERY common exhibition by street showmen, 
and one which never fails to excite surprise and 
draw a crowd, is the apparatus by which a person 
is apparently enabled to look through a brick. 
Mounted on a simple-looking stand are a couple of tubes 
which look like a telescope cut in two in the middle. Look- 

Fig. 34- 

ing through what most people take for a telescope, we are 
not surprised when we see clearly the people, buildings, 
trees, etc., beyond it, but this natural expectation is turned 
into the most startled surprise when it is found that the 
view of these objects is not cut off by placing a common 
brick between the two parts of the telescope and directly 
in the apparent line of vision, as shown in the accompany- 
ing illustration, Fig. 34. 



In truth, however, the observer looks round the brick 
instead of through it, and this he is enabled to do by means 
of four mirrors ingeniously arranged as shown in the en- 
graving. As the mirrors and the lower connecting tube 
are concealed, and the upright tubes supporting the pre- 
tended telescope, though hollow, appear to be solid, it is 
not very easy for those who are not in the secret to dis- 
cover the trick. 

Of course any number of "fake" explanations are given 
by the showman who always manages to keep up with the 
times and exploit the latest mystery. At one time it was 
psychic force, then Roentgen or X-ray s ; lately it has been 
attributed to the mysterious effects of radium ! 

This illustration is more properly a delusion ; there is no 
illusion about it. 



N Arabian author, Al Sephadi, relates the follow- 
ing curious anecdote : 

A mathematician named Sessa, the son of 
Dahar, the subject of an Indian Prince, having 
invented the game of chess, his sovereign was highly 
pleased with the invention, and wishing to confer on him 
some reward worthy of his magnificence, desired him to 
ask whatever he thought proper, assuring him that it should 
be granted. The mathematician, however, only asked for 
a grain of wheat for the first square of the chess-board, two 
for the second, four for the third, and so on to the last, or 
sixty-fourth. The prince at first was almost incensed at 
this demand, conceiving that it was ill-suited to his liberal- 
ity. By the advice of his courtiers, however, he ordered 
his vizier to comply with Sessa's request, but the minister 
was much astonished when, having caused the quantity of 
wheat necessary to fulfil the prince's order to be calculated, 
he found that all the grain in the royal granaries, and even 
all that in those of his subjects and in all Asia, would not 
be sufficient. 

He therefore informed the prince, who sent for the mathe- 
matician, and candidly acknowledged that he was not rich 
enough to be able to comply with his demand, the ingenuity 
of which astonished him still more than the game he had 

It will be found by calculation that the sixty-fourth term 
of the double progression, beginning with unity, is 




and the sum of all the terms of this double progression, 
beginning with unity, may be obtained by doubling the 
last term and subtracting the first from the sum. The 
number, therefore, of the grains of wheat required to sat- 
isfy Sessa's demand will be 


Now, if a pint contains 9,216 grains of wheat, a gallon 
will contain 73,728, and a bushel (8 gallons) will contain 
589,784. Dividing the number of grains by this quantity, 
we get 31,274,997,412,295 for the number of bushels nec- 
essary to discharge the promise of the Indian prince. And 
if we suppose that one acre of land is capable of producing 
in one year, thirty bushels of wheat, it would require 
1,042,499,913,743 acres, which is more than eight times 
the entire surface of the globe ; for the diameter of the 
earth being taken at 7,930 miles, its whole surface, in- 
cluding land and water, will amount to very little more 
than 126,437,889,177 square acres. 

If the price of a bushel of wheat be estimated at one 
dollar, the value of the above quantity probably exceeds 
that of all the riches on the earth. 


GENTLEMAN took a fancy to a horse, and the 
dealer, to induce him to buy, offered the animal 
for the value of the twenty-fourth nail in his 
shoe, reckoning one cent for the first nail, two 
for the second, four for the third, and so on. The gentle- 
man, thinking the price very low, accepted the offer. What 
was the price of the horse ? 


On calculating, it will be found that the twenty-fourth 
term of the progression i, 2, 4, 8, 16, etc., is 8,388,608, or 
$83,886.08, a sum which is more than any horse, even the 
best Arabian, was ever sold for. 

Had the price of the horse been fixed at the value of all 
the nails, the sum would have been double the above price 
less the first term, or $167,772.15. 


HE following note on the result of unrestrained 
propagation for one hundred generations is taken 
from "Familiar Lectures on Scientific Subjects," 
by Sir John F. W. Herschel : 
For the benefit of those who discuss the subjects of 
population, war, pestilence, famine, etc., it may be as well 
to mention that the number of human beings living at the 
end of the hundreth generation, commencing from a single 
pair, doubling at each generation (say in thirty years), and 
allowing for each man, woman, and child, an average space 
of four feet in height and one foot square, would form a 
vertical column, having for its base the whole surface of 
the earth and sea spread out into a plane, and for its height 
3,674 times the sun's distance from the earth ! The num- 
ber of human strata thus piled, one on the other, would 
amount to 460,790,000,000,000. 

In this connection the following facts in regard to the 
present population of the globe may be of interest : 

The present population of the entire globe is estimated 
by the best statisticians at between fourteen and fifteen 


hundred millions of persons. This number would easily 
find standing-room on one half of Long Island, in the State 
of New York. If this entire population were to be brought 
to the United States, we could easily give every man, 
woman, and child, one acre and a half each, or a nice little 
farm of seven acres and a half to every family, consisting 
of a man, his wife, and three children. 

This question has also an important bearing on the 
preservation of animals which, in limited numbers, are harm- 
less and even desirable. In Australia, where the restraints 
on increase are slight, the rabbit soon becomes not only a 
nuisance but a menace, and in this country the migratory 
thrush or robin, as it is generally called, has been so pro- 
tected in some localities that it threatens to destroy the 
small fruit industry. 


(ANY plans have been suggested for getting rich 
quickly, and some of these are so plausible and 
alluring that multitudes have been induced to 
invest in them the savings which had been accu- 
mulated by hard labor and severe economy. It is needless 
to say that, except in the case of a few stool-pigeons, who 
were allowed to make large profits so that their success 
might deceive others and lead them into the net, all these 
projects have led to disaster or ruin. It is a curious fact, 
however, that some of those who invested in such "get- 
rich-quickly" schemes were probably fully aware of their 
fraudulent character and went into the speculation with their 
eyes open in the hope that they might be allowed to become 


the stool-pigeons, and in this way come out of the enter- 
prise with a large balance on the right side. No regret 
can be felt when a bird of this kind gets plucked. 

But by the following simple method every one may 
become his own promoter and in a short time accumulate a 
respectable fortune. It would seem that almost any one 
could save one cent for the first day of the month, two cents 
for the second, four for the third, and so on. Now if you 
will do this for thirty days we will guarantee you the pos- 
session of quite a nice little fortune. See how easy it is 
to become a millionaire on paper, and by the way, it is only 
on paper that such schemes ever succeed. 

If, however, you should have any doubt in regard to your 
ability to lay aside the required amount each day, perhaps 
you can induce some prosperous and avaricious employer 
to accept the following tempting proposition : 

Offer to work for him for a year, provided he pays you one 
cent for the first week, two cents for the second, four for 
the third, and so on to the end of the term. Surely your 
services would increase in value in a corresponding ratio, 
and many business men would gladly accept your terms. 
We ourselves have had such a proposition accepted over 
and over again ; the only difficulty was that when we in- 
sisted upon security for the last instalment of our wages, 
our would-be employers could never come to time. And we 
would strongly urge upon our readers that if they ever 
make such a bargain, they get full security for the last 
payment for they will find that when it becomes due there 
will not be money enough in the whole world to satisfy the 

The entire amount of all the money in circulation among 
all the nations of the world (not the wealth} is estimated at 


somewhat less than $15,000,000,000, and the last payment 
would amount to fifteen hundred times that immense sum. 

The French have a proverb that " it is the first step 
that costs" (Jest le premier pas qui coute) but in this case 
it is the last step that costs and it costs with a vengeance. 

While on this subject let me suggest to my readers to 
figure up the amount of which they will be possessed if 
they will begin at fifteen years of age and save ten cents 
per week for sixty years, depositing the money in a savings 
bank as often as it reaches the amount required for a 
deposit, and adding the interest every six months. Most 
persons will be suprised at the result. 


EVEN years after the death of Shakespeare, his 
collected works were published in a large folio 
volume, now known as " The First Folio 
Shakespeare." This was in the year 1623. 
The price at which the volume was originally sold was 
one pound, but perhaps we ought to take into consideration 
the fact that at that time money had a value, or purchasing 
power, at least eight times that which it has at present ; 
Halliwell-Phillips estimates it at from twelve to twenty 
times its present value. For this circumstance, however, 
full allowance may be made by multiplying the ultimate 
result by the proper number. 

This folio is regarded as the most valuable printed book 
in the English language the last copy that was offered 


for sale in good condition having brought the record price 
of nearly $9,000, so that it is safe to assume that a perfect 
copy, in the condition in which it left the publisher's hands, 
would readily command $10,000, and the question now 
arises : What would be the comparative value of the present 
price, $10,000, and of the original price (one pound) placed 
at interest and compounded every year since 1623 ? 

Over and over again I have heard it said that the pur- 
chasers of the " First Folio " had made a splendid investment 
and the same remark is frequently used in reference to the 
purchase of books in general, irrespective of the present in- 
tellectual use that may be made of them. Let us make 
the comparison. 

Money placed at compound interest at six per cent, a 
little more than doubles itself in twelve years. At the 
present time and for a few years back, six per cent is a high 
rate, but it is a very low rate for the average. During a 
large part of the time money brought eight, ten, and twelve 
per cent per annum, and even within the half century just 
past it brought seven per cent during a large portion of 
the time. Now, between 1623 and 1899, there are 23 
periods, of 12 years each, and at double progression the 
twenty-third term, beginning with unity, would be 
8,388,608. This, therefore, would be the amount, in pounds, 
which the volume had cost up to 1 899. In dollars it would 
be $40,794,878.88. An article which costs forty millions 
of dollars, and sells for ten thousand dollars, cannot be 
called a very good financial investment. 

From a literary or intellectual standpoint, however, the 
subject presents an entirely different aspect, 

Some time ago I asked one of the foremost Shakesperian 
scholars in the world if he had a copy of the " First Folio." 


His reply was that he could not afford it ; that it would 
not be wise for him to lose $400 to $500 per year for the 
mere sake of ownership, when for a very slight expenditure 
for time and railway fare he could consult any one of half- 
a-dozen copies whenever he required to do so. 


GOOD-SIZED volume might be filled with the 
various arithmetical puzzles which have been 
propounded. They range from a method of 
discovering the number which any one may 
think of to a solution of the ''famous" question: "How 
old is Ann ? " Of the following cases one may be con- 
sidered a "catch" question, while the other is an interest- 
ing problem. 

A country woman, carrying eggs to a garrison where 
she had three guards to pass, sold at the first, half the 
number she had and half an egg more ; at the second, the 
half of what remained and half an egg more ; at the third 
the half of the remainder and half an egg more ; when she 
arrived at the market-place she had three dozen still to 
sell. How was this possible without breaking any of the 
eggs ? 

At first view, this problem seems impossible, for how 
can half an egg be sold without breaking any ? But by 
taking the greater half of an odd number we take the 
exact half and half an egg more. If she had 295 eggs 
before she came to the first guard, she would there sell 
148, leaving her 147. At the next she sold 74, leaving 
her 73. At the next she sold 37, leaving her three dozen. 


The second problem is as follows : After the Romans 
had captured Jotopat, Josephus and forty other Jews 
sought shelter in a cave, but the refugees were so fright- 
ened that, with the exception of Josephus himself and one 
other, they resolved to kill themselves rather than fall into 
the hands of their enemies. Failing to dissuade them from 
this horrid purpose, Josephus used his authority as their 
chief to insist that they put each other to death in an 
orderly manner. They were therefore arranged round a 
circle, and every third man was killed until but two men 
remained, the understanding being that they were to 
commit suicide. By placing himself and the other man 
in the 3ist and i6th places, they were the last that were 
left, and in this way they escaped death. 


EXT to that of Euclid, the name of Archimedes 
is probably that which is the best known of all 
the mathematicians and mechanics of antiquity, 
and this is in great part due to the two famous 
sayings which have been attributed to him, one being 
" Eureka" "I have found it," uttered when he dis- 
covered the method now universally in use for finding the 
specific gravity of bodies, and the other being the equally 
famous dictum which he is said to have addressed to Hiero, 
King of Sicily, " Give me a fulcrum and I will raise the 
earth from its place." 

That Archimedes, provided he had been immortal, could 
have carried out his promise, is mathematically certain, but 
it occurred to Ozanam to calculate the length of time which 


it would take him to move the earth only one inch, suppos- 
ing his machine constructed and mathematically perfect ; 
that is to say, without friction, without gravity, and in com- 
plete equilibrium, and the following is the result : 

For this purpose we shall suppose that the matter of 
which the earth is composed weighs 300 pounds per cubic 
foot, this being about the ascertained average. If the di- 
ameter of the earth be 7,930 miles, the whole globe will be 
found to contain 261,107,411,765 cubic miles, which make 
1,423,499,120,882,544,640,000 cubic yards, or 38,434,476,- 
263,828,705,280,000 cubic feet, arid allowing 300 pounds 
to each cubic foot, we shall have 11,530,342,879,148,611,- 
584,000,000 for the weight of the earth in pounds. 

Now, we know, by the laws of mechanics, that, whatever 
be the construction of a machine, the space passed over by 
the weight, is to that passed over by the moving power, in the 
reciprocal ratio of the latter to the former. It is known 
also, that a man can act with an effort equal only to about 
30 pounds for eight or ten hours, without intermission, 
and with a velocity of about 10,000 feet per hour. If 
then we suppose the machine of Archimedes to be put in 
motion by means of a crank, and that the force continually 
applied to it is equal to 30 pounds, then with the velocity 
of 10,000 feet per hour, to raise the earth one inch the 
moving power must pass over the space of 384,344,762,- 
638,287,052,800,000 inches; and if this space be divided 
by 10,000 feet or 120,000 inches, we shall have for a quo- 
tient 3,202,873,021,985,725,440, which will be the number 
of hours required for this motion. But as a year contains 
8,766 hours, a century will contain 876,600 ; and if we 
divide the above number of hours by the latter, the quo- 
tient, 3,653,745,176,803, will be the number of centuries 



during which it would be necessary to make the crank of 
the machine continually turn in order to move the earth 
only one inch. We have omitted the fraction of a cen- 
tury as being of little consequence in a calculation of this 
kind. The machine is also supposed to be constantly in 
action, but if it should be worked only eight hours each 
day, the time required would be three times as long. 

So that while it is true that Archimedes could move the 
world, the space through which he could have moved it, 
during his whole life, from infancy to old age, is so small 
that even if multiplied two hundred million times it could 
not be measured by even the most delicate of our modern 
measuring instruments. 

There is a modern saying which has become almost as 
famous amongst English-speaking peoples as is that of Ar- 
chimedes to the world at large. It is that which Bulwer 
Lytton puts into the mouth of Richelieu, in his well-known 
play of that name : 

" Beneath the rule of men entirely great 

About thirty years ago it occurred to the writer that 
these two epigrammatic sayings that of Archimedes and 
that of Bulwer Lytton, might be symbolized in an allegori- 
cal drawing which would forcibly express the ideas which 
they contain, and the question immediately arose Where 
will Archimedes get his fulcrum and what can he use as a 
lever ? 

And the mental answer was : Let the pen be the lever 
and the printing press the fulcrum, while the sword, used 
for the same purpose but resting on glory, or in other 
words, having no substantial fulcrum, breaks in the attempt. 


The little engraving which, with a new motto, forms a fit- 
ting tail-piece to this volume, was the outcome. 

It is true that the pen is mighty, and in the hands of 
philosophers and diplomats it accomplishes much, but it is 
only when resting on the printing press that it is provided 
with that fulcrum which enables it to raise the world by 
diffusing knowledge, inculcating morality, and providing 
pleasure and culture for humanity at large. 

When assigned to such a task the sword breaks, and 
well it may. But we have a well-grounded hope that 
through the influence of the pen and the printing press 
there will soon come an era of universal 

peace on JEartb anD <5ooD TOU Howard flfcen. 



Absurdities in perpetual motion . . 42 
Accuracy of modern methods of 

squaring the circle 17 

Adams, perpetual motion 71 

Ahaz, dial of 133 

Air, liquid 65 

Alkahest, or universal solvent ... 104 

Altar of Apollo 30 

Angelo, Michael, finely engraved seal 1 36 

Angle, Trisection of 33 

Apollo, Altar of 30 

Approximations to ratio of diameter 

to circumference of circle ... 17 

De Morgan's Illustration of . . 18 

New Illustration of 19 

Archimedean screw 49 

Archimedes, area of circle .... 13 

Ratio of circumference to diameter 14 

Archimedes and his fulcrum ... 171 

Arithmetic of the ancients .... 15 

Arithmetical problems 163 

Chess-board problem 163 

Nail problem 164 

A question of population .... 165 

How to become a millionaire . . 166 

Cost of first folio Shakespeare . 168 

Arithmetical puzzles 170 

Archimedes and his fulcrum . . 171 

Army Medical Museum 142 

Ball, Prof. W. W. R. 39, 129, 133, 134 

Balloons for conveying letters ... 147 
Balls proportion of weight to 

diameter 32 

Bean, jumping 128 

Bells kept ringing for eight years . 41 

Bible in walnut shell 136 

Bible, written at rate of 22 to square 

inch 141 

Boat-race without oars 129 

Bolognian phosphorus 102 


Boots lifting oneself by straps of 128 

Boyle and palingenesy 107 

Bramwell, Sir Frederick 38 

Brick, to look through 151 

Buckle and geometrical lines ... 119 
" Budget of Paradoxes," De Morgan, 

6, 18, 118 
Carbon bisulphide for perpetual 

motion 67 

Capillary attraction 53 

Carpenter, Edward fourth dimen- 
sion 122 

Catherine II 118 

" Century of Inventions " .... 74 

Chess-board problem 163 

Child lifting two horses 131 

Perpetual motion by a 64 

Circle, squaring the 9 

Supposed reward for squaring the 9 
Resolution of Royal Academy of 

Sciences on 10 

What the problem is 12 

Approximation to, by Archimedes 14 

Jews, ratio accepted by .... 13 

Egyptians, ratio accepted by . . 14 
Symbol for ratio introduced by 

Euler 14 

Graphical approximations. ... 22 
Circumference of circle, to find, when 

diameter is given 22 

Clock that requires no winding . . 38 

Columbia College seal 140 

Column of De Luc 40 

Compass, watch used as a .... 134 

Congreve, Sir William ...... 53 

Cube, duplication of 38 

Crystallization seen by microscope . 108 

Mistaken for palingenesy .... 100 

Dancer microphotographs 
Dangerous, fascination of the 






Declaration of Independence ... 145 

De Luc's column 40 

De Morgan Legend of Michael 

Scott 6 

Ignorance v. learning 8 

Illustration of accuracy of modern 

attempts to square the circle . 18 

" Budget of Paradoxes " ... 6, 18 

Trisection of angle 34, 118 

On powder of sympathy .... 112 

Anecdote of Diderot 118 

Dial of Ahaz 133 

Diderot, anecdote of 118 

Digby, Sir Kenelm, and palingenesy 109 
Sir Kenelm and powder of sym- 
pathy in 

Dircks 56, 71, 75 

Discoveries, valuable, not due to per- 
petual-motion-mongers .... 36 
Duplication of the cube 30 

Elixir of life 95 

Engineering, insect 130 

Euler 14, 118 

Fallacies in perpetual motion ... 65 

Falstaff and the philosopher's stone . 97 

Faraday's discovery 93 

Farrants, Prest. Royal Mic. Soc. . 140 

Figure, a, enlarged by cutting . . 126 

First folio Shakespeare, cost of . . 168 

Fixation of mercury 92 

Follies of Science, The Seven ... 2 

Disraeli's list 2 

An inappropriate term 3 

Fourth dimension conception of . 117 

Flatland 120 

Kant and Gauss 121 

Spiritualists 121 

Edward Carpenter on 122 

Possibility of a new sense ... 123 

Frauds in perpetual motion .... 69 

Freezing of mercury 93 

Froment, micrographs 139 

Gases, liquefication of 93 

Geiser's clock 71 

Geometrical quadrature impossible 21 

Gibberish, origin of word .... 96 

God, demonstration of existence of 118 

Hammer made of solid mercury . 93 


Hand, to look through 156 

Heat and cold, illusions 150 

Hesse, Landgrave of 77 

Hindoos, ratio accepted by .... 16 
Holmes, O. W., and powder of sym- 
pathy in 

Homer's Iliad in nut-shell .... 136 

Honecourt, Wilars de 42 

Horses lifted by child 131 

Hydrofluoric acid 104 

Hydrostatic paradox 46 

Iliad of Homer in nutshell .... 136 

Impossible, fascination of the ... i 

Insect engineering 130 

Irradiation 152 

Jews, ratio accepted by the ... 13 

Keeley gold cure 97 

Keeley motor 69 

Kircher and palingenesy 106 

Lacomme, on squaring circle ... 27 

Lamps, ever-burning 100 

Library, Congressional, in hand-bag 145 

Light from electric earth-currents . 103 

Lines, geometrical 119 

Lines, direction of, deceptive ... 154 

Length of, deceptive 153 

Liquid air 65 

Lodge, Sir Oliver, on conservation 

of energy 5 

Longitude, relation of squaring the 

circle to 10 

McArthur, on arithmetic of ancients 15 

Machin 16 

Magnetism for perpetual motion . 61 

Man lifting himself 128 

Mathematicians how they go to 

heaven 8 

Mercury, fixation of 9 2 

Freezing of 93 

Metals. See Transmutation. 

Metius, Peter 16 

Micrography, or minute writing . . 136 

Homer in a nutshell 136 

Michael Angelo's seal 136 

Ten Commandments 136 

Bible in a nutshell 136 




Micrography continued. 

Earliest micrographic engraving . 139 
Micrographic copy of seal of Co- 
lumbia College 139 

Peters' machine 141 

Lord's Prayer written at rate of 22 

Bibles to square inch .... 141 

Webb's fine writing 142 

Calculation in regard to .... 143 

Microphotographs by Dancer . . 144 
Pigeon- post in Franco-Prussian 

War 146 

Millionaire, to become a 166 

Miracle dial of Ahaz 133 

Morgan. See De Morgan. 

Morton, President Henry 66 

Motion, perpetual. See Perpetual 


Muir, Prof. On Archimedes ... 14 

Musitanus, Carolus 96 

Nail problem 164 

Nicomedean line 29 

Orffyreus his real name 77 

His fraudulent machine 77 

Overbalancing wheels 43 

Paint, luminous 102 

Palingenesy 106 

Patent office U. S. and perpetual 

motion 42 

Pen mightier than the sword ... 173 

Perpetual lamps 100 

Perpetual motion 36 

What the problem is 37 

Clock that requires no winding . 38 

Watch wound by walking ... 39 

Clock wound by tides 41 

By electricity 41 

Absurdities 42 

Overbalancing wheels 43 

Dr. Young, on 44 

Bellows action 45 

Hydrostatic paradox 46 

Bishop Wilkins 48 

Archimedean screw 49 

Archimedean screw, by mercury . 51 

Congreve's, by capillary attraction 53 

Tube and balls 56 

Tube and rope 59 

Magnetism . , 61 

Perpetual motion continued. 

Self-moving railway carriage . . 63 

A child's perpetual motion ... 64 

Fallacies 65 

Liquid air 65 

Bisulphide of carbon 66 

Frauds 69 

Keeley motor 69 

Geiser's clock 71 

Adams 71 

Redhoeffer 72 

Lukens 72 

How to stop the machine ... 73 

Marquis of Worcester 74 

Dircks' model 75 

Orffyreus 77 

Possibility of 78 

Peters' micrographs 141 

Philosopher's stone 97 

Phosphorus, discovery of 101 

Pigeon-post 146 

Population, a question of 165 

Power, the, of the future 40 

Ptolemy, on the circle 15 

Puzzles, arithmetical 170 

Railway carriage, self-moving ... 63 

Ramsay, Sir William 89, 98 

Ratio of diameter to circumference 

carried to 127 places 17 

Redhoeffer 's perpetual motion . . 72 

Rosicrucius 100 

Rutherford 16 

Schott, Father, and palingenesy . . 107 

Schweirs, Dr 52 

Scott, Michael, and his slave demons 6 
Scott, Sir Walter, legend of the 

great Wizard 6 

Powder of sympathy 112 

Self-moving railway carriage ... 63 

Senses illusions of 148 

Taste and smell 149 

Heat and cold 150 

Hearing 150 

Touch 150 

Sight size of spot 152 

Length of lines 153 

Direction of lines 154 

Objects seen through hand ... 156 

Looking through a brick .... 158 



1 68 

Sense, possibility of a new .... 
Shadow going backward on dial 
Shakespeare, cost of first folio . . 

Philosopher's stone 


Shanks value of ratio carried to 

707 places 16 

Sharp, Abraham 16 

Sight, sense of, deceived 152 

Smith, James, on squaring circle . 28 

Snake lifted by spider 130 

Solvent, universal 104 

Space enlarged by cutting 126 

Spider lifting a snake 130 

Sun-dial shadow going backward 133 

Taste and smell illusions .... 149 

Tides, clock moved by 40 

Will be the great source of power of 

the future 40 

Time it would take Archimedes to 

move the world 171 

Touch, sense of, deceived .... 150 

Transmutation of the metals ... 79 

Ancient fables 79 

Hermes Trismegistus 80 

Treatises not allegorical .... 81 

Seven metals 82 

Metals named after planets ... 82 


Transmutation of metals continued. 

Methods of cheating 83 

"Brief of the Golden Calf " . . 84 

Story of unknown Italian ... 87 

Possibility of effecting 88 

Sir William Ramsay 89 

Effect of such discovery on our 

currency system 90 

"Tribune," New York 29 

Trisection of angle 33 

Tube and balls 56 

Tube and rope 59 

Universal medicine. 

See Elixir of 

Van Ceulen, Rudolph 16 

Wallich, Dr 35 

Watch that is wound by walking . 39 

Used as a compass 134 

Webb micrographs 142 

WhewelPs refutation of 3^ ratio . . 28 

Wilkin's, Bishop 48 

Witchcraft or magic . 113 

Worcester, Marquis of 74 

Writing, fine 139 

Young, Dr. Thomas 44 





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